Question

Calculate to six decimal places the values of $\sqrt[3]{3{\left(\frac{294\times 125}{42\times 32}\right)}^2}$;
given $\log 2,\log 3,\log 7$; also $\log 9076.226=3.9579053$.

Answer 1

$\log \left(\sqrt[3]{3{\left(\frac{294\times 125}{42\times 32}\right)}^2}\right)$

$=\frac{2}{3}((2\log 7+\log 2+\log 3)+(3-3\log 2)-(\log 2+\log 3+\log 7)-5\log 2)$

$=0.9579053$

$=\log 9.076226$

$\Rightarrow \sqrt[3]{3{\left(\frac{294\times 125}{42\times 32}\right)}^2}=9.076226$