### All High School Math Resources

## Example Questions

### Example Question #6 : 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, .

### All High School Math Resources

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