Simplify the expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$.
A) 3
B) $- 9$
C) 0
D) $- 81$
E) The expression cannot be simplified.

Question

Quizplus · Accepted Answer

The expression simplifies to $\log_3(27^{-3})$. Since $27 = 3^3$, this becomes $\log_3((3^3)^{-3}) = \log_3(3^{-9})$. The logarithm of a number to its own base is the exponent, so this simplifies to $-9$.

Simplify the Expression log⁡3(127)3\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }log3​(271​)3

Simplify the Expression $\log _ { 3 } \left( \frac { 1 } { 27 } \right) ^ { 3 }$