Evaluating Logarithms with the Change of Base Formula

This video tutorial explains how to evaluate logarithms using the change of base formula. It begins by introducing the concept and demonstrating the formula: log base a of b equals log of b divided by log of a. The tutorial shows how to use a calculator to apply this formula, automatically converting to base 10. It includes examples to illustrate the process, such as evaluating log base 2 of 16 and other similar calculations.

What is the result of log base 2 of 16?

• 4

• 2

• 8

• 16

What does the change of base formula allow you to do?

• Multiply two logarithms

• Divide two numbers

• Change the base of the logarithm

• Change the exponent

If using the change of base formula with bases 5 and 12, what is crucial for the formula to work?

• The bases must be different

• The numbers must be integers

• Both logs must have the same base

• Both bases must be prime

What base does a calculator typically use when calculating logarithms if not specified?

• e

• 10

• 5

• 2

What is the result when you type 'log 16 divided by log 2' into a calculator?

• 4

• 16

• 2

• 8

Calculate log base 3 of 243 using the change of base formula.

• 3

• 4

• 6

• 5

What power of 3 gives 243?

• 6

• 3

• 5

• 4

Using the change of base formula, what is log base 7 of 343?

• 4

• 3

• 2

• 5

What power of 7 equals 343?

• 2

• 5

• 3

• 4

Why is the change of base formula useful in logarithmic calculations?

• It reduces computational errors

• It only works with base 10

• It allows any base to be used

• It simplifies multiplication