Evaluate without the use of a calculator. $$\log _ { 2 / 3 } \frac { 8 } { 27 }$$
A) 3
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 4 } { 9 }$

Question

Quizplus · Accepted Answer

The expression can be rewritten as $\log_{\frac{2}{3}}\left(\frac{2^3}{3^3}\right)$ or $\log_{\frac{2}{3}}\left(\left(\frac{2}{3}\right)^{-3}\right)$. The base and the argument are inverses of each other raised to the power of -3, thus the answer is 3.

Evaluate Without the Use of a Calculator log⁡2/3827\log _ { 2 / 3 } \frac { 8 } { 27 }log2/3​278​

Evaluate Without the Use of a Calculator $\log _ { 2 / 3 } \frac { 8 } { 27 }$