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If log2 x + logx 2 = 10/3 = log2 y +logy...

If `log_2 x + log_x 2 = 10/3 = log_2 y +log_y 2` and `x != y` find x+y

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`log_2^x+log_x^2=10/3`
`log_2^4+log_y^2`
`log_b^a=1/(log_a^b)`
`log_2^x+1/(log_2^x)=10/3=log_2^4+1/(log_2^4)`
Let `log_2^x=a`
`a+1/a=10/3`
`a=(1-pmsqrt(100-4*3*3))/2`
`a=(10pm8)/6=3+1/3`
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