### All Algebra II Resources

## Example Questions

### Example Question #1 : Simplifying Logarithms

Rewrite the following logarithmic expression in expanded form (i.e. as a sum and/or difference):

**Possible Answers:**

**Correct answer:**

By logarithmic properties:

;

Combining these three terms gives the correct answer:

### Example Question #2 : Simplifying Logarithms

Which of the following is equivalent to

?

**Possible Answers:**

**Correct answer:**

Recall that log implies base if not indicated.Then, we break up . Thus, we have .

Our log rules indicate that

.

So we are really interested in,

.

Since we are interested in log base , we can solve without a calculator.

We know that , and thus by the definition of log we have that .

Therefore, we have .

### Example Question #3 : Simplifying Logarithms

Find the value of the Logarithmic Expression.

**Possible Answers:**

**Correct answer:**

Use the change of base formula to solve this equation.

### Example Question #4 : Simplifying Logarithms

Many textbooks use the following convention for logarithms:

What is ?

**Possible Answers:**

**Correct answer:**

Remembering the rules for logarithms, we know that .

This tells us that .

This becomes , which is .

### Example Question #5 : Simplifying Logarithms

What is another way of expressing the following?

**Possible Answers:**

**Correct answer:**

Use the rule

### Example Question #6 : Simplifying Logarithms

Expand this logarithm:

**Possible Answers:**

**Correct answer:**

In order to solve this problem you must understand the product property of logarithms and the power property of logarithms . Note that these apply to logs of all bases not just base 10.

log of multiple terms is the log of each individual one:

now use the power property to move the exponent over:

### Example Question #7 : Simplifying Logarithms

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

We can rewrite the terms of the inner quantity. Change the negative exponent into a fraction.

This means that:

Split up these logarithms by addition.

According to the log rules, the powers can be transferred in front of the logs as coefficients.

The answer is: