Question

Given $\log 2$ and $\log 3$, find $\log (\sqrt[3]{348}\times {108}^{\frac{1}{4}}÷\sqrt[12]{126})$.

Answer 1

$\log \left(\frac{\sqrt[3]{348}\times \sqrt[4]{4108}}{\sqrt[12]{126}}\right)=\frac{1}{3}(\log 3+4\log 2)+\frac{1}{4}(2\log 2+3\log 3)-\frac{1}{12}(\log 2+\log 3)=1.00392381$