Find the value of the logarithmic expression.
-$$\log _ { 3 / 2 } \frac { 2 } { 3 }$$
A) 1
B) $- 1$
C) $- \frac { 1 } { 2 }$
D) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The logarithmic expression $\log _ { 3 / 2 } \frac { 2 } { 3 }$ can be interpreted as asking "to what power must $3/2$ be raised to get $2/3$?". Since $3/2$ and $2/3$ are reciprocals, raising $3/2$ to the power of $-1$ gives $2/3$. Therefore, the answer is $-1$.

Find the Value of the Logarithmic Expression log⁡3/223\log _ { 3 / 2 } \frac { 2 } { 3 }log3/2​32​

Find the Value of the Logarithmic Expression $\log _ { 3 / 2 } \frac { 2 } { 3 }$