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

  • 2
    $\begingroup$ 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

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


and substitute $y=\log_2x$, which gives


Then you have to use a numerical method to solve for $y$ and finally find $x$ by



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