Understanding Logarithms and the Change of Base Formula

This video tutorial explains how to use the change of base formula to evaluate logarithms using a calculator. It covers the formula's proof, demonstrates its application with examples, and reviews calculator functions for common and natural logs. The tutorial emphasizes the flexibility of choosing any base for calculations and verifies results through examples.

What does the Change of Base Formula allow you to do?

• Evaluate logarithms using any base

• Convert logarithms to exponential form

• Calculate the square root of a number

• Determine the derivative of a function

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CCSS.HSF.BF.B.5

Which two types of logarithms are commonly available on calculators?

• Log base 2 and log base 5

• Log base 10 and log base e

• Log base 3 and log base 7

• Log base 4 and log base 9

What is the first step in proving the Change of Base Formula?

• Add the logarithms together

• Multiply by the logarithm of the exponent

• Divide by the logarithm of the base

• Rewrite the logarithm in exponential form

Tags

CCSS.HSF.BF.B.5

What does a logarithm represent in mathematical terms?

• A sum

• A fraction

• An exponent

• A root

What is the result of raising e to the power of 3.6109?

• Approximately 20

• Approximately 30

• Approximately 50

• Approximately 37

How can you evaluate log base 7 of 89 using a calculator?

• Use the cube root of 89 divided by the cube root of 7

• Use the common log of 89 divided by the common log of 7

• Use the square root of 89 divided by the square root of 7

• Use the natural log of 89 divided by the natural log of 7

Which base is not typically available on standard calculators?

• Base 10

• Base e

• Base 2

• Base 7

What is the approximate value of log base 2 of 36?

• 4.1234

• 7.3456

• 6.2345

• 5.1699

What does the Change of Base Formula help with?

• Calculating integrals

• Finding the area of a circle

• Evaluating logarithms

• Solving quadratic equations

What is the purpose of using the Change of Base Formula?

• To simplify complex numbers

• To calculate derivatives

• To evaluate logarithms with bases not available on calculators

• To solve linear equations