How to evaluate a logarithm when it is raised to a power without a calculator

The video tutorial explains how to solve logarithmic problems using basic rules and properties. It begins with an introduction to logarithms, followed by a detailed explanation of the rules, such as log base five of five equals one, and log base five of five raised to the X equals X. The tutorial demonstrates how to evaluate logarithms by rewriting them in exponential form and using the one-to-one property of exponential equations. The video concludes with a summary of the evaluation process, emphasizing the importance of understanding these rules for solving logarithmic problems efficiently.

What is the value of log base five of five?

• 0

• 1

• 5

• 10

If log base five of five raised to the X equals X, what does this imply about the relationship between the base and the exponent?

• The base and exponent are unrelated.

• The base must be greater than the exponent.

• The base and exponent are equal.

• The exponent is always zero.

How can you rewrite a logarithm in exponential form?

• By dividing the base by the exponent.

• By adding the base and the exponent.

• By subtracting the exponent from the base.

• By setting the base raised to the exponent equal to the number.

What is the result of log base five of five raised to the seventh power?

• 35

• 5

• 1

• 7

Why is it unnecessary to show all the work when evaluating log base five of five raised to the seventh power?

• Because the exponent is always one.

• Because the base is always zero.

• Because the rule simplifies the process.

• Because the base and exponent are unrelated.