$\log_{10}\left(27\right)=3\log_{10}\left(x\right)$

$\log_{24}\left(x\right)+\log_{24}\left(x-2\right)=1$

$\log_{0.5}\left(8\right)$

$\:\left(sin2x+cos2x\right)^2=1+sin4x$

$\frac{1\:+\:\sin\:2\left(x\right)}{1\:+\:\cos\:2\left(x\right)}=\tan\left(x\right)\:+\:\frac{1}{2\cos^2\left(x\right)}$

$\int\frac{-14}{\left(2x+3\right)\left(x-1\right)}dx$

$s=\frac{\left(\left(e^x+e^y\right)^2-\left(e^x-e^y\right)^2\right)}{2e^xe^y}$