Question

Express ln√ab/c^3 as a sums and difference of logarithms.

Answer 1

\[\begin{align*}\ln\left(\frac{\sqrt{ab}}{c^3}\right)&=\ln\sqrt{ab}-\ln c^3\\
&=\ln{(ab)}^\frac{1}{2}-\ln c^3\\
&=\frac{1}{2}\ln(ab)-\ln c^3\\
&=\frac{1}{2}\left(\ln a + \ln b\right)-3\ln c\\
&=\frac{1}{2}\ln a + \frac{1}{2}\ln b-3\ln c\end{align*}\]

Answer 2

the problem is actually

Answer 3

Well, you should still be able to tell what properties were used in each step I gave. Why don't you try it out?