Express the following logarithm as specified.
-$\ln \sqrt { 4.5 }$ in terms of $\ln 3$ and $\ln 2$
A) $\frac { 2 \ln 3 + \ln 2 } { 2 }$
B) $\frac { 2 \ln 3 - \ln 2 } { 2 }$
C) $\frac { 2 \ln 3 } { 2 }$
D) $2 \ln 3$

Question

Quizplus · Accepted Answer

Use the property that $\ln a^{b} = b \ln a$ and simplify:
\begin{align*}
\ln \sqrt{4.5} &= \ln (4.5)^{\frac{1}{2}} \
&= \frac{1}{2} \ln 4.5 \
&= \frac{1}{2} \ln (9\div2) \
&= \frac{1}{2} (\ln 9 - \ln 2) \
&= \frac{1}{2} (2 \ln 3 - \ln 2) \
&= \frac{2\ln 3 - \ln 2}{2}
\end{align*}

Express the Following Logarithm as Specified ln⁡4.5\ln \sqrt { 4.5 }ln4.5​

Express the Following Logarithm as Specified $\ln \sqrt { 4.5 }$