Question

1) 8^ (2/x)=4 solve for x 2)25^ (1/x+3) = 1/5 solve for x

Answer 1

1)

$8^{\frac{2}{x}}=4\\\\2^{3(\frac{2}{x})}=2^{2}\\\\ \dfrac{6}{x}=2\\\\ \dfrac{6}{2}=x=3$

2)

$\displaystyle 25^{\left(\frac{1}{x}+3\right)}=\frac{1}{5}\\\\ 5^{2\left(\frac{1}{x}+3\right)}=5^{-1}\\\\ 2\left(\frac{1}{x}+3\right)=-1\\\\ \frac{2}{x}=-7\\\\ \frac{2}{-7}=x=-\frac{2}{7}$

or

$\displaystyle 25^{\left(\frac{1}{x+3}\right)}=\frac{1}{5}\\\\ 5^{2\left(\frac{1}{x+3}\right)}=5^{-1}\\\\ 2\left(\frac{1}{x+3}\right)=-1\\\\ \frac{2}{-1}=x+3\\\\ -5=x$