Question

Evaluvate $\frac{1}{4}\log 3+\log \frac{3}{2}$

Answer 1

$\frac{1}{4}\log 3+\log \frac{3}{2}$

$=\log 3^{\frac{1}{4}}+\log \frac{3}{2}$

$=\log 3^{\frac{1}{4}}+\log 3-\log 2$

$=\log 3^{\frac{1}{4}+1}-\log 2$

$=\log 3^{\frac{5}{4}}-\log 2$

$=\frac{5}{4}\log 3-\log 2$