Rewrite the ratio as a ratio of natural logarithms and simplify.
-$\frac { \log _ { 2 } x } { \log _ { 16 } x }$
A) $\frac { 1 } { 2 ^ { 3 } }$
B) $2 ^ { 3 }$
C) $\ln 4$
D) 4

Question

Quizplus · Accepted Answer

Using the change of base formula for logarithms, we can rewrite the given ratio as $\frac{\ln x / \ln 2}{\ln x / \ln 16}$. Simplifying this gives $\frac{\ln 16}{\ln 2}$, which simplifies further to $\ln 2^{4} / \ln 2 = 4$.

Rewrite the Ratio as a Ratio of Natural Logarithms and Simplify