The second method for solving exponential equations involves using logarithms. For example, when trying to solve 3^{x} = 11, 3 and 11 cannot be written as like bases. The log of both sides will need to be determined.

Example 1 Solve the equation

Step 1. Since there is no common base, apply logarithms.

In this example, common logs were used but any base can be used.

Step 2. Use the Power to a Power Property.

Step 3. Solve for x.

*Note: If starting with a different base, the Change of Base Property will create this same equation.

Step 4. Use a calculator to find the answer.

Step 5. Make sure to check the answer:

*Note: Since the value of x was rounded to three decimal places it creates a round-off error (a slightly inaccurate answer when checked).