Question

Express
$2log5\sqrt{5}+3log2-log50-1$ as a single logarithm.

Answer 1

$2log5\sqrt{5}+3log2-log50-1$

$\Rightarrow log(5\sqrt{5}{)}^2+log{2}^3-log50-log10$

$\Rightarrow log\left(\frac{5\sqrt{5}\times 5\sqrt{5}\times 2\times 2\times 2}{50\times 10}\right)$

$\Rightarrow log\left(\frac{25\times 5\times 8}{50\times 10}\right)$

$\Rightarrow log2$.