Question

Solve ${\log }_{10}{(3!+2!\times 6!-9!÷7!)}^{-3}$

Answer 1

We have,

${\log }_{10}{(3!+2!\times 6!-9!÷7!)}^{-3}$

$\Rightarrow {\log }_{10}{(3!+2!\times 6!-\frac{9!}{7!})}^{-3}$

$\Rightarrow {\log }_{10}{(6+2\times 6\times 5\times 4\times 3\times 2\times 1-\frac{9\times 8\times 7!}{7!})}^{-3}$

$\Rightarrow {\log }_{10}{(6+1440-72)}^{-3}$

$\Rightarrow -3{\log }_{10}\left(1374\right)$

$\Rightarrow -3{\log }_{10}\left(1374\right)$

$\Rightarrow -3\times 3.13798$

$\Rightarrow -9.414$

Hence, this is the answer.