# High School Math : Solving Logarithmic Equations

## Example Questions

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### Example Question #1 : Solving Logarithmic Equations

Solve the equation.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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 .

Explanation:

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.

Explanation:

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.

Explanation:

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,

### Example Question #9 : Solving Logarithmic Equations

Solve the equation.

Explanation:

Change the right side to  so that both sides have the same bsae of 10. Apply log and then set the exponential expressions equal to each other

### Example Question #10 : Solving Logarithmic Equations

Solve the equation.