Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 468: 9

$x=log_{\frac{1}{2}}(12)$ $x=\frac{log12}{log\frac{1}{2}}$ $x=\frac{ln12}{ln\frac{1}{2}}$

Step 1. For $(\frac{1}{2})^x=12$, use the meaning of logarithm to get $x=log_{\frac{1}{2}}(12)$ Step 2. Use the change-of base theorem to write the result of step 1 as $x=\frac{log12}{log\frac{1}{2}}$ Step 3. Use the change-of base theorem to write the result of step 1 as $x=\frac{ln12}{ln\frac{1}{2}}$