Logarithmic and exponential equation.

Question

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 04 '13 at 20:25

score 2 · Answer 1 · answered Jun 04 '13 at 20:42

If the expression is correct, then the only thing you can do is notice that

$$\log_x2=\frac{1}{\log_2x}$$

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

$$x=2^y$$

1 Answers1