Exponentials
Method 2
The second method for solving exponential equations involves using logarithms. For example, when trying to solve 3x = 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.
![Method2Ex1-2 Method2Ex1-2](https://claregladwinresd.glk12.org/pluginfile.php/953/mod_book/chapter/338/Exponential_and_Logarithmic_Functions/Images/Method2Ex1-2.png)
In this example, common logs were used but any base can be used.
Step 2. Use the Power to a Power Property.
![Method2Ex1-3 Method2Ex1-3](https://claregladwinresd.glk12.org/pluginfile.php/953/mod_book/chapter/338/Exponential_and_Logarithmic_Functions/Images/Method2Ex1-3.png)
Step 3. Solve for x.
![Method2Ex1-4 Method2Ex1-4](https://claregladwinresd.glk12.org/pluginfile.php/953/mod_book/chapter/338/Exponential_and_Logarithmic_Functions/Images/Method2Ex1-4.png)
*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.
![Method2Ex1-5 Method2Ex1-5](https://claregladwinresd.glk12.org/pluginfile.php/953/mod_book/chapter/338/Exponential_and_Logarithmic_Functions/Images/Method2Ex1-5.png)
Step 5. Make sure to check the answer:
![Method2Ex1-6 Method2Ex1-6](https://claregladwinresd.glk12.org/pluginfile.php/953/mod_book/chapter/338/Exponential_and_Logarithmic_Functions/Images/Method2Ex1-6.png)
*Note: Since the value of x was rounded to three decimal places it creates a round-off error (a slightly inaccurate answer when checked).