Question

What should be the value of $x$, such that it satisfies the equation $4^x=\frac{\sqrt{16}}{256}$ ?

• A. 3
• B. -3
• C. 4
• D. 2

Answer 1

The correct option is B -3

Consider the equation $4^x=\frac{\sqrt{16}}{256}$
$⟹256\times 4^x=\sqrt{16}$
But, $256=4^4$ and $\sqrt{16}=4.$
$⟹4^4\times 4^x=4^1$
$⟹4^{4+x}=4^1(\because a^m\times a^n=a^{m+n})$

Since the bases are equal, their powers must also be equal.
$⟹4+x=1$
$⟹x=-3$