High School Math : Using Logarithms with Exponents

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Using Logarithms With Exponents

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 #2 : Using Logarithms With Exponents

Solve for

Possible Answers:

Correct answer:

Explanation:

Use the power reducing theorem:

and

Example Question #3 : Using Logarithms With Exponents

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 #4 : Using Logarithms With Exponents

Simplify the expression below. 

 

Possible Answers:

Correct answer:

Explanation:

Based on the definition of exponents, .

Then, we use the following rule of logarithms: 

Thus, 

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