simple problem

-

x=4 doesnt satisfy.
x=2^{\sqrt{2}}

ans given is (2^-√2,2^√2)

thanks Aditya

but please explain how you got the statement log₂4x =log₂x . log₂2x

@mohit....

by inverting the denominator and numerator on both sides we get the above result...

You can simply convert log₂x as logx /log2
so the expression will be quadratic in terms of log x
i.e.
log2 = 1
logx(logx+log2) (2log2 + logx)

you know how to solve further