Combining log terms

Question

I have this particular problem. We have to combine the log terms into a single log term:

$$\dfrac{(2\ln a- \ln b - 5\ln c)}{2}$$

I did it in the following way :

$$''~= \ln a -\frac{1}{2}\ln b - \frac{5}{2} \ln c$$ $$= \ln\left(\left(\frac{a^2c^5}{b}\right)^{\frac{1}{2}}\right)$$

Is this correct approach?

I used the formula : $\log_ba-\log_bc=\log_b\left(\dfrac{a}{c}\right)$

Answer 1

$$\dfrac{(2\ln a- \ln b - 5\ln c)}{2}$$ $$ =\dfrac{(\ln a^2- \ln b - \ln c^5)}{2} $$ $$= \dfrac{\left(\ln \dfrac{a^2}{b} - \ln c^5\right)}{2} $$ $$= \dfrac{1}{2}\ln \dfrac{a^2}{bc^5} $$ $$= \ln \dfrac{a}{\sqrt{bc^5}}$$