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Easy Ways to Solve Log and Exponential Equations

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Easy Ways to Solve Log and Exponential Equations
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Max Luke

@maxluke

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A comprehensive guide to solving logarithmic and exponential equations strategies with detailed examples and methods.

  • Master the fundamental approaches including isolation, condensing, and the common base method for solving exponential equations
  • Learn essential techniques for isolating and condensing logs in equations through step-by-step examples
  • Understand how to check for extraneous solutions and domain restrictions
  • Practice with various equation types including natural logarithms and exponential forms
  • Apply systematic problem-solving strategies across different logarithmic scenarios

1/11/2023

94

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

View

Page 2: Advanced Logarithmic Equation Techniques

This section delves into more complex logarithmic equations and demonstrates various solution methods. The page emphasizes the importance of proper logarithm manipulation and condensing techniques.

Vocabulary: Condensing logarithms refers to combining multiple logarithmic terms into a single logarithm.

Example: In solving log₈(x+2) = log₈(3x-2), the equation can be solved by setting the arguments equal: x+2 = 3x-2.

Highlight: The solution process often involves converting logarithmic equations to exponential form or vice versa.

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

View

Page 3: Natural Logarithms and Exponential Solutions

This page covers equations involving natural logarithms (ln) and the exponential function (e). It demonstrates how to solve equations containing these special functions.

Definition: Natural logarithm (ln) is the logarithm with base e, where e is Euler's number (approximately 2.71828).

Example: For ln(3x+5) = 8, the solution involves using e⁸ = 3x+5, then solving for x.

Highlight: Domain restrictions are particularly important when solving natural logarithmic equations.

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

View

Page 4: Complex Exponential Equations

The focus here is on solving more complicated exponential equations, particularly those that result in quadratic equations after manipulation.

Example: For eˣ²+2x=0, the solution involves factoring (eˣ-2)(eˣ-1)=0 and solving two separate equations.

Vocabulary: Quadratic form in exponential equations occurs when the variable appears in two different powers.

Highlight: When solving exponential equations, converting to logarithmic form can often simplify the solution process.

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

View

Page 5: Advanced Applications and Combined Techniques

This final page demonstrates complex problems that combine multiple concepts and techniques from previous sections.

Example: For log(x²+1) = log(x-2) + log(x+3), the solution requires condensing logarithms and solving the resulting polynomial equation.

Highlight: Final verification of solutions is crucial to ensure they satisfy both the equation and domain restrictions.

Quote: "Check for extraneous solutions when solving logarithmic equations to ensure validity of answers."

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

View

Page 1: Core Strategies for Solving Logarithmic and Exponential Equations

This page introduces the fundamental strategies for solving logarithmic and exponential equations. The content focuses on three main approaches: isolation of logarithms, comparing equal logarithms, and identifying common bases in exponential equations.

Definition: Logarithmic equations are equations that contain logarithms of variables, while exponential equations contain variables in the exponent.

Highlight: When solving logarithmic equations, always check for extraneous solutions due to domain restrictions.

Example: For exponential equations like bˣ = bʸ, the solution is x = y when using the common base method.

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Condensing Logarithms lesson notes

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Subjects

/

Pre-Calculus

/

Binomial Theorem

/

The Binomial Theorem

Easy Ways to Solve Log and Exponential Equations

user profile picture

Max Luke

@maxluke

·

3 Followers

Follow

A comprehensive guide to solving logarithmic and exponential equations strategies with detailed examples and methods.

  • Master the fundamental approaches including isolation, condensing, and the common base method for solving exponential equations
  • Learn essential techniques for isolating and condensing logs in equations through step-by-step examples
  • Understand how to check for extraneous solutions and domain restrictions
  • Practice with various equation types including natural logarithms and exponential forms
  • Apply systematic problem-solving strategies across different logarithmic scenarios

1/11/2023

94

 

11th

 

Pre-Calculus

2

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

Page 2: Advanced Logarithmic Equation Techniques

This section delves into more complex logarithmic equations and demonstrates various solution methods. The page emphasizes the importance of proper logarithm manipulation and condensing techniques.

Vocabulary: Condensing logarithms refers to combining multiple logarithmic terms into a single logarithm.

Example: In solving log₈(x+2) = log₈(3x-2), the equation can be solved by setting the arguments equal: x+2 = 3x-2.

Highlight: The solution process often involves converting logarithmic equations to exponential form or vice versa.

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

Page 3: Natural Logarithms and Exponential Solutions

This page covers equations involving natural logarithms (ln) and the exponential function (e). It demonstrates how to solve equations containing these special functions.

Definition: Natural logarithm (ln) is the logarithm with base e, where e is Euler's number (approximately 2.71828).

Example: For ln(3x+5) = 8, the solution involves using e⁸ = 3x+5, then solving for x.

Highlight: Domain restrictions are particularly important when solving natural logarithmic equations.

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

Page 4: Complex Exponential Equations

The focus here is on solving more complicated exponential equations, particularly those that result in quadratic equations after manipulation.

Example: For eˣ²+2x=0, the solution involves factoring (eˣ-2)(eˣ-1)=0 and solving two separate equations.

Vocabulary: Quadratic form in exponential equations occurs when the variable appears in two different powers.

Highlight: When solving exponential equations, converting to logarithmic form can often simplify the solution process.

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

Page 5: Advanced Applications and Combined Techniques

This final page demonstrates complex problems that combine multiple concepts and techniques from previous sections.

Example: For log(x²+1) = log(x-2) + log(x+3), the solution requires condensing logarithms and solving the resulting polynomial equation.

Highlight: Final verification of solutions is crucial to ensure they satisfy both the equation and domain restrictions.

Quote: "Check for extraneous solutions when solving logarithmic equations to ensure validity of answers."

4.5 Notes Solving Thursday, September 23, 2021 Notes 9/23 4.5: Solving Log + Exp. Equations Strategies / Scenarios Isolate 4 (5) 9:47 AM log

Page 1: Core Strategies for Solving Logarithmic and Exponential Equations

This page introduces the fundamental strategies for solving logarithmic and exponential equations. The content focuses on three main approaches: isolation of logarithms, comparing equal logarithms, and identifying common bases in exponential equations.

Definition: Logarithmic equations are equations that contain logarithms of variables, while exponential equations contain variables in the exponent.

Highlight: When solving logarithmic equations, always check for extraneous solutions due to domain restrictions.

Example: For exponential equations like bˣ = bʸ, the solution is x = y when using the common base method.

Similar Content

Pre-Calculus - Condensing Logarithms lesson notes

Notes on how to condense logarithms with examples and explanations of the steps for pre calculus

1

14

0

Know Condensing Logarithms lesson notes thumbnail

Pre-Calculus - Pascal's Triangle and Binomial Theorem

How to expand polynomials using Pascal's Triangle and Binomial Theorem. Important to note: Pascals triangle can be expanded further, only the first 5 levels are shown.

5

93

0

Know Pascal's Triangle and Binomial Theorem thumbnail

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.

Ranked #1 Education App

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