# Logarithmic and exponential equation.

Find $x$ in $$\large3^{\log_{2} {x}} +3^{\log_{x} {2}}=90$$

• Please verify that this expression is copied correctly, as it does not appear to have a nice exact solution as written. – vadim123 Jun 4 '13 at 20:25

$$\log_x2=\frac{1}{\log_2x}$$
and substitute $y=\log_2x$, which gives
$$3^y+3^{1/y}=90$$
Then you have to use a numerical method to solve for $y$ and finally find $x$ by
$$x=2^y$$