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Explanation:

log₂x × log(x/64)² = log(x/16)²

$\therefore \frac{\log x}{\log 2}\times \frac{\log 2}{\log \left({\displaystyle \frac{x}{64}}\right)}=\frac{\log 2}{\log \left({\displaystyle \frac{x}{16}}\right)}$

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).