Use a calculator and the change-of-base formula to find the logarithm to four decimal places. $$\log _ { \frac { 1 } { 3 } } 3$$
A)0.5769
B)- 1.0000
C)1.1005
D)- 1.0078
E)1.7654

Question

Quizplus · Accepted Answer

The change-of-base formula allows us to convert the given logarithm to a more familiar base, such as 10 or e. Using base 10, we have $\log_{\frac{1}{3}}3 = \frac{\log_{10}3}{\log_{10}(\frac{1}{3})}$. Simplifying this gives $\frac{\log_{10}3}{-\log_{10}3}$, which equals -1. Therefore, the correct answer is -1.0000.

Use a Calculator and the Change-Of-Base Formula to Find the Logarithm