# Algebra II : Solving and Graphing Logarithms

## Example Questions

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### Example Question #1 : Solving Logarithms

Solve for :

Explanation:

To solve for , first convert both sides to the same base:

Now, with the same base, the exponents can be set equal to each other:

Solving for  gives:

### Example Question #2 : Solving Logarithms

Solve the equation:

Explanation:

### Example Question #3 : Solving Logarithms

Use    to approximate the value of  .

Explanation:

Rewrite  as a product that includes the number :

Then we can split up the logarithm using the Product Property of Logarithms:

Thus,

.

### Example Question #4 : Solving Logarithms

Solve for .

Explanation:

Rewrite in exponential form:

Solve for x:

### Example Question #5 : Solving Logarithms

Solve the following equation:

Explanation:

For this problem it is helpful to remember that,

is equivalent to  because

Therefore we can set what is inside of the parentheses equal to each other and solve for  as follows:

### Example Question #6 : Solving Logarithms

Solve for :

Explanation:

To solve this logarithm, we need to know how to read a logarithm. A logarithm is the inverse of an exponential function. If a exponential equation is

then its inverse function, or logarithm, is

Therefore, for this problem, in order to solve for , we simply need to solve

which is .

### Example Question #7 : Solving Logarithms

Solve for .

Explanation:

Logs are exponential functions using base 10 and a property is that you can combine added logs by multiplying.

You cannot take the log of a negative number.  x=-25  is extraneous.

### Example Question #8 : Solving Logarithms

If  , which of the following is a possible value for ?

Explanation:

This question is testing the definition of logs.  is the same as .

In this case,  can be rewritten as .

Taking square roots of both sides, you get . Since only the positive answer is one of the answer choices,  is the correct answer.

### Example Question #9 : Solving Logarithms

Rewriting Logarithms in Exponential Form

Solve for  below:

Which of the below represents this function in log form?

Explanation:

The first step is to rewrite this equation in log form.

When rewriting an exponential function as a log we must remember that the form of an exponential is:

When this is rewritten in log form it is:

.

Therefore we have  which when rewritten gives us,

.

### Example Question #10 : Solving Logarithms

Solve for :

.

Not enough information

Explanation:

Use the rule of Exponents of Logarithms to turn all the multipliers into exponents:

.

Simplify by applying the exponents: .

According to the law for adding logarithms, .

Therefore, multiply the 4 and 7.

.

Because both sides have the same base, .

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