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

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

$$x=2^y$$

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