Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 468: 10

$x=log_{\frac{1}{3}}(4)$ $x=\frac{log4}{log\frac{1}{3}}$ $x=\frac{ln4}{ln\frac{1}{3}}$

Step 1. For $(\frac{1}{3})^x=4$, use the meaning of logarithm to get $x=log_{\frac{1}{3}}(4)$ Step 2. Use the change-of base theorem to write the result of step 1 as $x=\frac{log4}{log\frac{1}{3}}$ Step 3. Use the change-of base theorem to write the result of step 1 as $x=\frac{ln4}{ln\frac{1}{3}}$