High School Math : Exponential and Logarithmic Functions

Example Questions

Example Question #1 : Logarithmic Functions

You are given that  and

Which of the following is equal to  ?

Explanation:

Since  and , it follows that  and

Explanation:

Example Question #2 : Solving Logarithms

What is

Explanation:

Recall that by definition a logarithm is the inverse of the exponential function. Thus, our logarithm corresponds to the value of  in the equation:

We know that  and thus our answer is .

Example Question #1 : Simplifying Logarithms

Solve for

The correct solution set is not included among the other choices.

The correct solution set is not included among the other choices.

Explanation:

FOIL:

These are our possible solutions. However, we need to test them.

:

The equation becomes . This is true, so  is a solution.

:

However, negative numbers do not have logarithms, so this equation is meaningless.  is not a solution, and  is the one and only solution. Since this is not one of our choices, the correct response is "The correct solution set is not included among the other choices."