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## Course: Algebra 2 Â  > Â  Unit 6

Solving exponential equations using exponent properties.

• Solve exponential equations using exponent properties
• Solving exponential equations using exponent properties (advanced)
• Solve exponential equations using exponent properties (advanced)
• Rational exponents and radicals: FAQ

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• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics
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## Most Used Actions

Number line.

• 8^{x-2}=\sqrt{8}
• 10^{1-x}=10^4
• 6^{3x}=2^{2x-3}
• 3^x=9^{x+5}
• What is an exponential equation?
• An exponential equation is an equation that contains an exponential expression of the form b^x, where b is a constant (called the base) and x is a variable.
• How do you solve exponential equations?
• To solve an exponential equation start by isolating the exponential expression on one side of the equation. Then, take the logarithm of both sides of the equation to convert the exponential equation into a logarithmic equation. The logarithm must have the same base as the exponential expression in the equation. Use logarithmic properties to simplify the logarithmic equation, and solve for the variable by isolating it on one side of the equation.
• What is an exponent?
• An exponent is a mathematical notation indicating the number of times a value is multiplied by itself.
• what is e in math?
• In mathematics, 'e' refers to the mathematical constant approximately equal to 2.71828. It is widely used in various mathematical and scientific fields, such as exponential and logarithmic functions.
• Is log the inverse of exponential?
• Logarithm and exponential are inverse functions. If y = b^x, where b is the base of the exponential, then x = logb(y).

exponential-equation-calculator

• High School Math Solutions – Exponential Equation Calculator Solving exponential equations is pretty straightforward; there are basically two techniques: <ul> If the exponents... Read More

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## About solving equations

A value is said to be a root of a polynomial if ..

The largest exponent of appearing in is called the degree of . If has degree , then it is well known that there are roots, once one takes into account multiplicity. To understand what is meant by multiplicity, take, for example, . This polynomial is considered to have two roots, both equal to 3.

One learns about the "factor theorem," typically in a second course on algebra, as a way to find all roots that are rational numbers. One also learns how to find roots of all quadratic polynomials, using square roots (arising from the discriminant) when necessary. There are more advanced formulas for expressing roots of cubic and quartic polynomials, and also a number of numeric methods for approximating roots of arbitrary polynomials. These use methods from complex analysis as well as sophisticated numerical algorithms, and indeed, this is an area of ongoing research and development.

Systems of linear equations are often solved using Gaussian elimination or related methods. This too is typically encountered in secondary or college math curricula. More advanced methods are needed to find roots of simultaneous systems of nonlinear equations. Similar remarks hold for working with systems of inequalities: the linear case can be handled using methods covered in linear algebra courses, whereas higher-degree polynomial systems typically require more sophisticated computational tools.

## How Wolfram|Alpha solves equations

For equation solving, Wolfram|Alpha calls the Wolfram Language's Solve and Reduce functions, which contain a broad range of methods for all kinds of algebra, from basic linear and quadratic equations to multivariate nonlinear systems. In some cases, linear algebra methods such as Gaussian elimination are used, with optimizations to increase speed and reliability. Other operations rely on theorems and algorithms from number theory, abstract algebra and other advanced fields to compute results. These methods are carefully designed and chosen to enable Wolfram|Alpha to solve the greatest variety of problems while also minimizing computation time.

Although such methods are useful for direct solutions, it is also important for the system to understand how a human would solve the same problem. As a result, Wolfram|Alpha also has separate algorithms to show algebraic operations step by step using classic techniques that are easy for humans to recognize and follow. This includes elimination, substitution, the quadratic formula, Cramer's rule and many more.

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## How to Solve Math Problems

Last Updated: May 16, 2023 Fact Checked

This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 573,808 times.

Although math problems may be solved in different ways, there is a general method of visualizing, approaching and solving math problems that may help you to solve even the most difficult problem. Using these strategies can also help you to improve your math skills overall. Keep reading to learn about some of these math problem solving strategies.

## Understanding the Problem

• Draw a Venn diagram. A Venn diagram shows the relationships among the numbers in your problem. Venn diagrams can be especially helpful with word problems.
• Draw a graph or chart.
• Arrange the components of the problem on a line.
• Draw simple shapes to represent more complex features of the problem.

## Expert Q&A

• Seek help from your teacher or a math tutor if you get stuck or if you have tried multiple strategies without success. Your teacher or a math tutor may be able to easily identify what is wrong and help you to understand how to correct it. Thanks Helpful 1 Not Helpful 1
• Keep practicing sums and diagrams. Go through the concept your class notes regularly. Write down your understanding of the methods and utilize it. Thanks Helpful 1 Not Helpful 0

## You Might Also Like

• â Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
• â http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
• â https://math.berkeley.edu/~gmelvin/polya.pdf

To solve a math problem, try rewriting the problem in your own words so it's easier to solve. You can also make a drawing of the problem to help you figure out what it's asking you to do. If you're still completely stuck, try solving a different problem that's similar but easier and then use the same steps to solve the harder problem. Even if you can't figure out how to solve it, try to make an educated guess instead of leaving the question blank. To learn how to come up with a solid plan to use to help you solve a math problem, scroll down! Did this summary help you? Yes No

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of a Pentagonal Prism • Volume of a Prism • Volume of a Pyramid • Volume of a Right Circular Cone • Volume of a Sphere • Volume of a Square Box • Volume of a Triangular Pyramid • Volume of Cube • Volume of Cuboid • Volume of Hemisphere • Volume of Rectangular Prism • Volume of Rectangular Pyramid • What Are Perfect Numbers • What Is a Billion? • What is a Coefficient in Math • What Is a Constant • What is a Number Chart? • What is a Set in Math • What is Estimation in Maths? • What is LBS to KG? • What is Radius of a Circle? • What is the Circumference of the Earth? Calculation, Examples • What is Y Intercept? • Whole numbers • X And Y – Axis • X Intercept • Xcoordinate • Ycoordinate • Zero Product Property • Zero property of multiplication ## Number e Explained We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. ## Easy Finger Math Tricks to Help Kids Solve Problems Posted: November 9, 2023 | Last updated: November 9, 2023 While using your fingers isn't the fastest way to recall a multiplication fact while doing a problem, finger math tricks can help kids figure out how to answer the problem at hand âÂ and as they work on their math, they will eventually learn all the facts by repetition. Note that before your child can understand other finger tricks, theyÂ must be able to count by 2s, 5s, and 10s and multiply by 2s, 3s, and 4s. ## Quick Finger Math Tricks for ThreesÂ and Fours The tricks for multiplying by threesÂ and foursÂ are really a matter of counting out the answer on your fingers. As your children count out the answer repeatedly, they'll memorize it and then be able to move on to larger numbers. ## Multiplying by Three Did you realize that all of your fingers have three segments? Therefore, you can figure out anything from 3 x 1 to 3 x 10 by counting the segments on each finger. To start: • Hold up the number of fingers you're going to multiply by 3. For example, if the problem is 3 x 4 âÂ hold up four fingers. • Count each segment on each finger you're holding up, and you should come up with 12 âÂ which is the correct answer. ## Multiplying by Four Multiplying by four is the same as multiplying by two âÂ twice. To start: • Hold up the number of fingers to correspond with the number you are multiplying by four. For example, if you are multiplying 4 x 6 âÂ hold up six fingers. • Count each finger by two, moving from left to right. Then count each finger again, continuing to count by twos, until you've counted every finger twice. Helpful Hack To keep track of the fingersÂ you've counted twice, sometimes it's easier to put your finger down as you count the first time, and back up as you count the second time. ## Finger Math Tricks for Multiplying by 6, 7, 8, and 9 While numbers one through five are easy for most kids to remember, six and up often pose a problem. This handy trick will make it a little easier to work those problems out. ## Multiplying 6, 7, 8, and 9 by Hand To begin, assign each finger a number. For example, your thumbs represent 6, your index fingers each represent 7, etc. This will remain the same throughout the finger math hack. Your left hand will represent the first number that you are multiplying and your right hand will represent the second number you are multiplying. In this example, we are multiplying 7 x 8.Â To Determine the Part ofÂ Your Answer: • On your left hand, put down the finger that represents the number you are multiplying as well as any fingers whose number value is less than this figure. In this example, you are multiplying 7 x 8, so the left hand will represent 7. You will drop your index finger (number 7) and your thumb (number 6). • Similarly, the right hand will represent eight, so you will drop down your middle finger (number 8), your index finger (number 7), and your thumb (number 6). • Now, just multiply the fingers that are still pointed upwards. In this case, you will have three fingers on your left hand and two on your right, so you will multiply 3Â x 2Â to get 6. This is the first part of your answer! To Determine the Second Part of Your Answer: • Keeping your fingers in the same positions, count how many fingers are folded down. In the 7 x 8 example, you should have five fingers folded.Â • You will count each of these in quantities of ten. So, 10, 20, 30, 40, 50. • 50 is your answer. To Determine Your Final Answer: • Add your two numbers together. In this example, you would add 6 + 50, whichÂ gives you 56! ## Another Finger Math Trick Just for Nine There is a trick that works separately, just for multiplying by the number nine. • To start, hold up all ten fingers, with your palms facing you. • Assign each finger a number, starting with your left-hand thumb and ending with your right-hand thumb. The left-hand thumb will be one, the left-hand index finger will be two, and so on until you reach the number 10 for your right-hand thumb. • To tackle a problem, put down the corresponding finger of the number you're multiplying by nine. For example, if you are multiplying 9 x 8, you'd put down the eighthÂ finger (which will be on your right hand). • Count all the fingers to the left of the finger you have folded down. This will give you 7. This is the first digit of your answer. • Count all the fingers to the right of the finger you have folded down. This will give you 2. This is the second digit of your answer. • Put the numbers together! Your answer is 72. ## Finger Multiplication Tricks Can Make Math Easy and Fun While the hope is that your kids will eventually memorize their multiplication charts , using some quick hand tricks for multiplicationÂ and letting them count things out on their fingers is not a bad way to learn. It keeps frustration at bay since the answer is always a fingertip away, and the repetition of having to figure it out will help cement those facts into their brains. ## More for You Mike Lindell Cheers Judge's 'Historic' Ruling as Vindication Experts raise alarm after Biden strikes agreement with China to shut down fossil fuels Iran's betrayal leaves Hamas nowhere to go Balance of Nature ordered to stop sales of supplements after FDA lawsuits Pluggers by Rick McKee Chilling map shows the utter devastation of a nuclear attack on the US Newly released audio reveals Trumpâs words about January 6 crowd Itâs not just a stereotype: Gen Z really does âhave a work ethic problemâ The seven new types of old age â and how to tell which one you are How to watch tonight's Colorado Buffaloes vs. Washington State Cougars game: Livestream options, kickoff time Animal Crackers by Mike Osbun A Russian official said soldiers are dying in large numbers, but he'll get in trouble if he doesn't send more to fight, leaked video shows Donald Trump's Interactions With Secret Service on Jan. 6 Revealed in Audio The flu is soaring in seven US states and rising in others, health officials say Here Are All the States That Donât Tax Social Security Benefits The Best Burger in Every State Zoolies by Jonny Hawkins 'Unusually heavy' rains caused Rolling Hills Estates landslide, city report shows CNN analyst: Report on California grand jury âbad newsâ for Hunter Biden The Strange Silence of Louis Farrakhan on Israel-Hamas War ## Nerd AI - Tutor & Math Helper 4+ Powered by chatgpt api, codeway dijital hizmetler anonim sirketi, designed for iphone. • #6 in Education • 4.7 âą 8.7K Ratings • Offers In-App Purchases ## iPhone Screenshots Description. Powered by the latest AI technology, Nerd AI is here to help you breeze through your studies. With a range of powerful features, Nerd AI transforms the way you approach writing, problem-solving, language learning, summarizing, coding, and expanding your knowledge on any topic. SCAN AND SOLVE Snap a photo of your question and get answers in a second with step-by-step explanations. WRITE EFFORTLESSLY Say goodbye to the writing struggles and hello to a world of effortless creativity. With our cutting-edge features, you can generate compelling essays, captivating blogs, and polished presentation scripts with utmost ease. Customize the word count and writing tone to match your requirements or cater to your specific audience perfectly. IMPROVE LANGUAGE SKILLS Ready to level up your language skills? Nerd AI has got your back! Our intelligent grammar hints and text translation tools will help you become a linguistic maestro. 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I recommend you do actually get this app if you want to have step-by-step explanations which can get you ahead in your class. ## Itâs actually good I thought this was another one of those big scams to pay money to access the app. Itâs not the case here. I can only ask and scan, but thatâs even useful. I love this. 1000% recommend. ## App Privacy The developer, Codeway Dijital Hizmetler Anonim Sirketi , indicated that the appâs privacy practices may include handling of data as described below. For more information, see the developerâs privacy policy . ## Data Used to Track You The following data may be used to track you across apps and websites owned by other companies: ## Data Linked to You The following data may be collected and linked to your identity: ## Data Not Linked to You The following data may be collected but it is not linked to your identity: • User Content • Identifiers • Diagnostics Privacy practices may vary, for example, based on the features you use or your age. LearnÂ More ## Information • Weekly Subscription$4.99
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The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

## Older Adults and Balance Problems

Have you ever felt dizzy, lightheaded, or as if the room were spinning around you? These can be troublesome sensations. If the feeling happens often, it could be a sign of a balance problem.

## Causes of balance problems

Symptoms of balance disorders, treatments for balance problems and disorders, coping with a balance disorder.

Many older adults experience problems with balance and dizziness. Problems can be caused by certain medications, balance disorders, or other medical conditions. Balance problems are one reason older people fall. Maintaining good balance as you age and learning about fall prevention can help you get around, stay independent, and carry out daily activities.

People are more likely to have problems with balance as they grow older. In some cases, you can help reduce your risk for certain balance problems, but problems often can start suddenly and without obvious cause.

Balance problems can be caused by certain medications or medical conditions. The list below covers some common causes of balance problems.

• Medications. Check with your doctor if you notice balance problems while taking certain medications. Ask if other medications can be used instead, if the dosage can be safely reduced, or if there are other ways to reduce unwanted side effects.
• Inner ear problems. A part of the inner ear called the labyrinth is responsible for balance. When the labyrinth becomes inflamed, a condition called labyrinthitis occurs, causing vertigo and imbalance. Certain ear diseases and infections can lead to labyrinthitis.
• Alcohol. Alcohol in the blood can also cause dizziness and balance problems by affecting how the inner ear works.
• Other medical conditions. Certain conditions, such as diabetes, heart disease, stroke , or problems with your vision, thyroid, nerves, or blood vessels can cause dizziness and other balance problems.

Visit the NIHÂ National Institute on Deafness and Other Communication DisordersÂ website for more information on specific balance disorders .

If you have a balance disorder, you might experience symptoms such as:

• Dizziness or vertigo (a spinning sensation)
• Falling or feeling as if you are going to fall
• Staggering when you try to walk
• Lightheadedness, faintness, or a floating sensation
• Blurred vision
• Confusion or disorientation

Other symptoms might include nausea and vomiting; diarrhea; changes in heart rate and blood pressure and feelings of fear, anxiety, or panic. Symptoms may come and go over short periods or last for a long time and can lead to fatigue and depression.

Exercises that involve moving the head and body in certain ways can help treat some balance disorders. Patient-specific exercises are developed by a physical therapist or other professional who understands balance and its relationship with other systems in the body.

Balance problems due to high blood pressure may be managed by eating less salt (sodium), maintaining a healthy weight , and exercising . Balance problems due to low blood pressure may be managed by drinking plenty of fluids such as water; avoiding alcohol ; and being cautious regarding your bodyâs posture and movement, such as never standing up too quickly. Consult with your doctor about making any changes in your diet or activity level.

Some people with a balance disorder may not be able to fully relieve their dizziness and will need to find ways to cope with it. A vestibular rehabilitation therapist can help develop an individualized treatment plan.

Chronic balance problems can affect all aspects of your life, including your relationships, work performance, and your ability to carry out daily activities. Support groups provide the opportunity to learn from other people with similar experiences and challenges.

If you have trouble with your balance, talk to your doctor about whether itâs safe to drive, and about ways to lower your risk of falling during daily activities, such as walking up or down stairs, using the bathroom, or exercising. To reduce your risk of injury from dizziness, do not walk in the dark. Avoid high heels and, instead, wear nonskid, rubber-soled, low-heeled shoes. Donât walk on stairs or floors in socks or in shoes and slippers with smooth soles. If necessary, use a cane or walker. Make changes to add safety features at your home and workplace, such as adding handrails.

Read about this topic in Spanish . Lea sobre este tema en espaĂ±ol .

## You may also be interested in

• Learning more about falls and falls prevention
• Find out more about ways to prevent falls in certain rooms
• Watching a video on balance exercises

MedlinePlus National Library of MedicineÂ Â Â Â Â Â  www.medlineplus.gov

Mayo Clinic www.mayoclinic.org/patient-care-and-health-information

National Institute on Deafness and Other Communication Disorders 800-241-1044 800-241-1055 (TTY) [email protected] www.nidcd.nih.gov

This content is provided by the NIH National Institute on Aging (NIA). NIA scientists and other experts review this content to ensure it is accurate and up to date.

Content reviewed: September 12, 2022

nia.nih.gov

An official website of the National Institutes of Health

## Game Central

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6. E 2 Solving Equations using mental math

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23. Older Adults and Balance Problems

Many older adults experience problems with balance and dizziness. Problems can be caused by certain medications, balance disorders, or other medical conditions. Balance problems are one reason older people fall. Maintaining good balance as you age and learning about fall prevention can help you get around, stay independent, and carry out daily ...

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