Determine the function value.
-Suppose $f ( x ) = \log _ { a } x$ and $f ( 4 ) = 2$. Find $f \left( \frac { 1 } { 16 } \right)$
A) $- 4$
B) $\frac { 1 } { 2 }$
C) $- 2$
D) 4

Question

Quizplus · Accepted Answer

Given $f(4) = 2$, this means $\log_a(4) = 2$, implying $a^2 = 4$. Therefore, $a = 2$ (since $a$ is positive in logarithmic functions). To find $f\left(\frac{1}{16}\right) = \log_2\left(\frac{1}{16}\right)$, recognize that $2^{-4} = \frac{1}{16}$, so $\log_2\left(\frac{1}{16}\right) = -4$.

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