### All High School Math Resources

## Example Questions

### Example Question #3 : Simplifying Logarithms

Which of the following expressions is equivalent to ?

**Possible Answers:**

**Correct answer:**

According to the rule for exponents of logarithms,. As a direct application of this,.

### Example Question #4 : Simplifying Logarithms

Simplify the expression below.

**Possible Answers:**

**Correct answer:**

Based on the definition of exponents, .

Then, we use the following rule of logarithms:

Thus, .

### Example Question #1 : Solving Logarithmic Equations

Solve the equation.

**Possible Answers:**

**Correct answer:**

Change 81 to so that both sides have the same base. Once you have the same base, apply log to both sides so that you can set the exponential expressions equal to each other (). Thus, .

### Example Question #2 : Solving Logarithmic Equations

Solve the equation.

**Possible Answers:**

**Correct answer:**

Change the left side to and the right side to so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other (). .

### Example Question #3 : Solving Logarithmic Equations

Solve the equation.

**Possible Answers:**

**Correct answer:**

Change the left side to and the right side to so that both sides have the same base. Apply log and then set the exponential expressions equal to each other (). Thus, .

### Example Question #4 : Solving Logarithmic Equations

Solve the equation.

**Possible Answers:**

**Correct answer:**

Change the left side to and the right side to so that both sides have the same base. Apply log and then set the exponential expressions equal to each other (). Thus,

### Example Question #5 : Solving Logarithmic Equations

Solve the equation.

**Possible Answers:**

**Correct answer:**

Change the left side to and the right side to so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other (). Thus, .

### Example Question #6 : Solving Logarithmic Equations

Solve for .

**Possible Answers:**

**Correct answer:**

can be simplified to since . This gives the equation:

Subtracting from both sides of the equation gives the value for .

### Example Question #7 : Solving Logarithmic Equations

Solve the equation.

**Possible Answers:**

**Correct answer:**

First, change 25 to so that both sides have the same base. Once they have the same base, you can apply log to both sides so that you can set their exponents equal to each other, which yields .

### Example Question #8 : Solving Logarithmic Equations

Solve the equation.

**Possible Answers:**

**Correct answer:**

Change 49 to so that both sides have the same base so that you can apply log. Then, you can set the exponential expressions equal to each other .

Thus,

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