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Explanation:

log2x × log(x/64)2 = log(x/16)2

log xlog 2×log 2log x64=log 2log x16

It is clear that x has to be a power of 2 to solve the equation i.e. x ≠ 12.

Hence, option (c) is eliminated.

If x = 16, then the base of the RHS (i.e. x/16) becomes 1, which is not possible for a logarithm i.e. x ≠ 16. Hence, option (d) is eliminated.

If x = 2, then you get (x/64) = (x/16); which is not possible.

Hence, x = 4

Hence, option (b).

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