Question

Simplify $2log3-\frac{1}{2}log16+log12$.

Answer 1

$$\begin{array}{c}2\log 3-\frac{1}{2}\log 16+\log 12\\ =log{3}^2+\log {16}^{\frac{1}{2}}+\log 12\left[a\log b=\log b^a\right]\\ =\log 9+\log 4+\log 12\\ =\log 9\times 4\times 12\left[\log k+\log h=\log k\times h\right]\\ =\log 3^3\cdot 2^4=3\log 3+4\log 2\end{array}$$