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Course: Algebra 2   >   Unit 6

Solving exponential equations using exponent properties.

  • Solve exponential equations using exponent properties
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  • 8^{x-2}=\sqrt{8}
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  • 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).


  • 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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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

Step 1 Identify the type of 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.

Step 5 Look for patterns.

Developing a Plan

Step 1 Figure out what formulas you will need to solve the problem.

Solving the Problem

Step 1 Follow your plan.

Expert Q&A

Daron Cam

  • 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

how to solve math problems with e

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Do Math Proofs

  • ↑ Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
  • ↑ http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies
  • ↑ http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
  • ↑ https://math.berkeley.edu/~gmelvin/polya.pdf

About This Article

Daron Cam

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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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 — 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, they must be able to count by 2s, 5s, and 10s and multiply by 2s, 3s, and 4s.

Quick Finger Math Tricks for Threes and Fours

The tricks for multiplying by threes and fours 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 — hold up four fingers.
  • Count each segment on each finger you're holding up, and you should come up with 12 — which is the correct answer.

Multiplying by Four

Multiplying by four is the same as multiplying by two — 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 — 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 fingers 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. 

To Determine the Part of 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 3 x 2 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. 
  • 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, which 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 eighth 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 multiplication 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.

child counting fingers

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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. REWRITE Shape your words like a pro with Nerd AI's rewriting capabilities. Whether you need to paraphrase, simplify, continue texts, or fine-tune your writing drafts, we've got you covered. Make your writing shine and convey your thoughts with precision. LEARN TO CODE Do you want to learn to code but have no idea where to start? No problem! Nerd AI provides comprehensive assistance with any programming language. Understand the logic behind any code as Nerd AI explains it and take your coding skills to new heights. Input your code, and Nerd AI will check and optimize it for you, paving the way for coding success! TRIVIA QUEST: Knowledge is power, and Nerd AI loves to challenge your intellect! Engage in stimulating trivia quests covering a wide range of topics. Feel the power of Nerd AI as it transforms the way you write, learn languages, summarize texts, rewrite content, and delve into the world of coding. Download now and experience the joy of seamless learning and creativity! Privacy Policy: https://static.nerdai.app/privacy-en.html Terms of Use: https://static.nerdai.app/terms-conditions-en.html

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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.

On this page:

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.

Six Tips To Help Prevent Falls infographic. Click link in caption to see full transcript.

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 NIH National Institute on Deafness and Other Communication Disorders website for more information on specific balance disorders .

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

Older woman using a walker on a sidewalk

  • 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 body’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 it’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. Don’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 español .

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

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For more information on balance problems.

MedlinePlus National Library of Medicine       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


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