Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
-$\log _ { \sqrt { 3 } } 96.4$
A) 0.120
B) 8.317
C) 4.158
D) 0.239

Question

Quizplus · Accepted Answer

The Change-of-Base Formula allows us to rewrite the logarithm in a form that can be calculated using a calculator, typically as a natural logarithm or a common logarithm. The formula is $\log_b a = \frac{\log_c a}{\log_c b}$, where $c$ can be any positive value, but we often use 10 or $e$ for convenience. Using this formula, we can rewrite the given logarithm as $\log_{\sqrt{3}} 96.4 = \frac{\log 96.4}{\log \sqrt{3}}$. Using a calculator to evaluate this expression and rounding to three decimal places gives us approximately 8.317.

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