Find the value of the logarithmic expression.
-$\log _ { 4 } \frac { 1 } { 16 }$
A) 2
B) $- 2$
C) $- \frac { 1 } { 4 }$
D) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The expression $\log_4 \frac{1}{16}$ can be rewritten as $\log_4 16^{-1}$. Since $16 = 4^2$, this becomes $\log_4 (4^2)^{-1} = \log_4 4^{-2}$. The logarithm of a number to its own base is the exponent, so this simplifies to $-2$.

Find the Value of the Logarithmic Expression log⁡4116\log _ { 4 } \frac { 1 } { 16 }log4​161​

Find the Value of the Logarithmic Expression $\log _ { 4 } \frac { 1 } { 16 }$