Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
$\log _ { \frac { 1 } { 3 } } 6$
A)-0.631
B)2.369
C)0.369
D)-1.631
E)1.369

Question

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places.
 $\log _ { \frac { 1 } { 3 } } 6$ 
A)-0.631
B)2.369
C)0.369
D)-1.631
E)1.369

Quizplus · Accepted Answer

The change-of-base formula is $\log_b a = \frac{\log_c a}{\log_c b}$. Using base 10, $\log_{\frac{1}{3}} 6 = \frac{\log_{10} 6}{\log_{10} \frac{1}{3}}$. Calculating this gives approximately -1.631.

Evaluate the Logarithm Using the Change-Of-Base Formula log⁡136\log _ { \frac { 1 } { 3 } } 6log31​​6

Evaluate the Logarithm Using the Change-Of-Base Formula $\log _ { \frac { 1 } { 3 } } 6$