Subjects

Math (ACT®)

Preparation and Review

Exponents and Logarithms

Exploring Exponential Functions and Logarithms for Kids

Name: Knowunity
Brand: Knowunity

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Exploring Exponential Functions and Logarithms for Kids

Ahmed Nour ✓™

@ahmednour

414 Followers

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

179

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: logₐ(x×y) = logₐx + logₐy
Division law: logₐ(x÷y) = logₐx - logₐy
Power law: logₐ(xⁿ) = n×logₐx

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

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:

Take log of both sides
Apply power law
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.

View

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 f(x) = aˣ is a function where a constant is raised to a variable power.

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

Example: For the function f(x) = eˣ, its derivative f'(x) = 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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

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Subjects

Math (ACT®)

Preparation and Review

Exponents and Logarithms

Exploring Exponential Functions and Logarithms for Kids

Ahmed Nour ✓™

@ahmednour

414 Followers

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

179

11th/12th

Math (ACT®)

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: logₐ(x×y) = logₐx + logₐy
Division law: logₐ(x÷y) = logₐx - logₐy
Power law: logₐ(xⁿ) = n×logₐx

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

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:

Take log of both sides
Apply power law
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.

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 f(x) = aˣ is a function where a constant is raised to a variable power.

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

Example: For the function f(x) = eˣ, its derivative f'(x) = 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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User