Question

Expand the following

log$\left[e^x{\left(\frac{x-2}{x+2}\right)}^{3/4}\right]$

Answer 1

$\log \left[e^x{\left(\frac{x-2}{x+2}\right)}^{3/4}\right]\Rightarrow \log e^x+\log {\left(\frac{x-2}{x+2}\right)}^{3/4}$

$\Rightarrow x\log e+\frac{3}{4}log\left(\frac{x-2}{x+2}\right)$

$\Rightarrow x\log e+\frac{3}{4}\left\{log\right(x-2)-log(x+2\left)\right\}$

$\Rightarrow x+\frac{3}{4}log(x-2)-\frac{3}{4}\left(log\right(x+2\left)\right)$