Question

Simplify: $\frac{1}{2}\log 9+\frac{1}{3}\log 27$

Answer 1

$\begin{array}{c}\frac{1}{2}\log 9+\frac{1}{3}\log 27\\ =\log 9^{\frac{1}{2}}+\log {27}^{\frac{1}{3}}\\ =\log {\left(3^2\right)}^{\frac{1}{2}}+\log {\left(3^3\right)}^{\frac{1}{3}}\\ =\log 3+\log 3\\ =\log 3\times 3\\ =\log 9\end{array}$