Express the following logarithm as specified.
-$\ln 2 \sqrt { 2 }$ in terms of $\ln 2$ and $\ln 3$
A) $\ln 3 + \frac { \ln 2 } { 2 }$
B) $\frac { \ln 2 } { 2 }$
C) $\frac { 3 } { 2 } \ln 2$
D) $\ln 2 + \frac { \ln 2 } { 2 }$

Question

Quizplus · Accepted Answer

The expression $\ln 2 \sqrt { 2 }$ can be rewritten using logarithmic properties as $\ln 2 + \ln \sqrt { 2 }$. Since $\sqrt { 2 } = 2^{1/2}$, $\ln \sqrt { 2 } = \frac { 1 } { 2 } \ln 2$. Therefore, the expression simplifies to $\ln 2 + \frac { 1 } { 2 } \ln 2 = \frac { 3 } { 2 } \ln 2$.

Express the Following Logarithm as Specified ln⁡22\ln 2 \sqrt { 2 }ln22​

Express the Following Logarithm as Specified $\ln 2 \sqrt { 2 }$