Find the value of the logarithm without using a calculator.
-$\log _ { 9 } \frac { 1 } { 81 }$
A) 2
B) $- 2$
C) 9
D) $- 9$

Question

Quizplus · Accepted Answer

The expression $\log_9 \frac{1}{81}$ can be rewritten as $\log_9 9^{-2}$ because $81 = 9^2$ and taking the reciprocal of a base to a power is equivalent to changing the sign of the exponent. Therefore, $\log_9 9^{-2} = -2$, since the logarithm of a number to its own base is the exponent, in this case, $-2$.

Find the Value of the Logarithm Without Using a Calculator log⁡9181\log _ { 9 } \frac { 1 } { 81 }log9​811​

Find the Value of the Logarithm Without Using a Calculator $\log _ { 9 } \frac { 1 } { 81 }$