Evaluate the logarithm. $\log _ { 5 } \frac { 1 } { 125 }$
A) $\sqrt { 3 }$
B) -3
C)0
D) $\frac { 1 } { 3 }$
E) $\log _ { 5 } \frac { 1 } { 125 }$ is undefined.

Question

Quizplus · Accepted Answer

Remember that $\log_{5} \left(\frac{1}{125}ight) = x$ can be rewritten as $5^{x} = \frac{1}{125}$. We know that $125$ can be written as $5^{3}$, so we have $5^{x} = \frac{1}{5^{3}} = 5^{-3}$. Thus, $x = -3$. Therefore, the answer is $\boxed{	extbf{(B)}\ -3}$.

Evaluate the Logarithm log⁡51125\log _ { 5 } \frac { 1 } { 125 }log5​1251​

Evaluate the Logarithm $\log _ { 5 } \frac { 1 } { 125 }$