Question

Simplify: $\frac{\log 8+\log \sqrt{27}-\log \sqrt{1000}}{\log \left(1.2\right)}$

Answer 1

$\frac{log8+log\sqrt{27}-log\sqrt{1000}}{log\left(1.2\right)}$

$\Rightarrow \frac{log{2}^3+log{27}^{1/2}-log{1000}^{1/2}}{log\frac{12}{10}}$

$\Rightarrow \frac{3log2+log{3}^{3\times 1/2}-lo{g}^{3\times 1/2}}{log12-log10}$

$\Rightarrow \frac{3log2+\frac{3}{2}log3-\frac{3}{2}log10}{log4+log3-log10}$

$\Rightarrow \frac{\frac{3}{2}(2log2+log3-log10)}{log{2}^2+log3-log10}$

$\Rightarrow \frac{\frac{3}{2}(2log2+log3-log10)}{(2log2+log3-log10)}$

$\Rightarrow \frac{3}{2}$ Ans