High School Math : Using Logarithms with Exponents

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Simplifying Logarithms

Evaluate by hand 

Possible Answers:

Cannot be found by hand

Correct answer:

Explanation:

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm.  This expression can be simplified as 

Example Question #7 : Simplifying Logarithms

Solve for

Possible Answers:

Correct answer:

Explanation:

Use the power reducing theorem:

and

Example Question #8 : Simplifying Logarithms

Which of the following expressions is equivalent to

Possible Answers:

Correct answer:

Explanation:

According to the rule for exponents of logarithms,. As a direct application of this,.

Example Question #9 : Simplifying Logarithms

Simplify the expression below. 

 

Possible Answers:

Correct answer:

Explanation:

Based on the definition of exponents, .

Then, we use the following rule of logarithms: 

Thus, 

Learning Tools by Varsity Tutors