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Exploring Exponential Functions and Logarithms for Kids

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Ahmed Nour ✓™

9/16/2023

Math (ACT®)

Exponentials and logarithms

Exploring Exponential Functions and Logarithms for Kids

A comprehensive guide to exponential functions and their gradients, covering properties of natural logarithms and solving logarithmic equations with examples.

  • Exponential functions of form f(x) = aˣ pass through point (0,1) and approach zero as x decreases
  • Natural logarithms and exponential functions demonstrate unique derivative properties where f(x) = eˣ has f'(x) = eˣ
  • Logarithmic laws include multiplication, division, and power properties essential for equation solving
  • Complex logarithmic equations can be solved through careful application of logarithmic properties and laws
  • Practical applications include converting non-linear relationships to linear form for analysis
...

9/16/2023

187

exponential functions
f(x) = ax
always go through I
on x-axis
tends towards
0 as
x decreases
graphs of their gradient functions are similar

View

Page 2: Logarithmic Laws and Properties

The second page delves into the essential laws and properties of logarithms, providing a foundation for solving logarithmic equations.

Definition: The logarithm of a number is the power to which a base must be raised to produce that number.

Highlight: Key logarithmic laws include:

  • Multiplication law: logₐx×yx×y = logₐx + logₐy
  • Division law: logₐx÷yx÷y = logₐx - logₐy
  • Power law: logₐxnxⁿ = n×logₐx

Example: If 3² = 9, then log₃9 = 2, demonstrating the relationship between exponentials and logarithms.

exponential functions
f(x) = ax
always go through I
on x-axis
tends towards
0 as
x decreases
graphs of their gradient functions are similar

View

Page 3: Mixed Exercises and Applications

The final page presents various exercises applying logarithmic and exponential concepts, demonstrating practical problem-solving techniques.

Example: Solving 4ˣ = 2³ involves using logarithms:

  1. Take log of both sides
  2. Apply power law
  3. Solve for x using log properties

Highlight: When solving logarithmic equations, always check solutions as logarithms of negative numbers are undefined.

Vocabulary: The term "linear data" refers to data that forms a straight line when plotted, often achieved by applying logarithmic transformations to exponential relationships.

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Math (ACT®)

187

Sep 16, 2023

3 pages

Exploring Exponential Functions and Logarithms for Kids

user profile picture

Ahmed Nour ✓™

@ahmednour

A comprehensive guide to exponential functions and their gradients, covering properties of natural logarithms and solving logarithmic equations with examples.

  • Exponential functions of form f(x) = aˣ pass through point (0,1) and approach zero as x decreases
  • Natural... Show more

exponential functions
f(x) = ax
always go through I
on x-axis
tends towards
0 as
x decreases
graphs of their gradient functions are similar

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Page 2: Logarithmic Laws and Properties

The second page delves into the essential laws and properties of logarithms, providing a foundation for solving logarithmic equations.

Definition: The logarithm of a number is the power to which a base must be raised to produce that number.

Highlight: Key logarithmic laws include:

  • Multiplication law: logₐx×yx×y = logₐx + logₐy
  • Division law: logₐx÷yx÷y = logₐx - logₐy
  • Power law: logₐxnxⁿ = n×logₐx

Example: If 3² = 9, then log₃9 = 2, demonstrating the relationship between exponentials and logarithms.

exponential functions
f(x) = ax
always go through I
on x-axis
tends towards
0 as
x decreases
graphs of their gradient functions are similar

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Mixed Exercises and Applications

The final page presents various exercises applying logarithmic and exponential concepts, demonstrating practical problem-solving techniques.

Example: Solving 4ˣ = 2³ involves using logarithms:

  1. Take log of both sides
  2. Apply power law
  3. Solve for x using log properties

Highlight: When solving logarithmic equations, always check solutions as logarithms of negative numbers are undefined.

Vocabulary: The term "linear data" refers to data that forms a straight line when plotted, often achieved by applying logarithmic transformations to exponential relationships.

exponential functions
f(x) = ax
always go through I
on x-axis
tends towards
0 as
x decreases
graphs of their gradient functions are similar

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Exponential Functions and Natural Logarithms

This page introduces fundamental concepts of exponential functions and their relationship with logarithms. The content explores the basic properties and behaviors of these mathematical functions.

Definition: An exponential function fxx = aˣ is a function where a constant is raised to a variable power.

Highlight: All exponential functions pass through the point 0,10,1 on the coordinate plane and approach zero as x decreases.

Example: For the function fxx = eˣ, its derivative f'xx = eˣ, demonstrating the unique property of the natural exponential function.

Vocabulary: The number 'e' is a special mathematical constant approximately equal to 2.71828, often called Euler's number.

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Greenlight Bonnie

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I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

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Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user