Question

If $4^{{\sqrt{x}}^{\sqrt{x}}}=256$, the value of x is:

• A. 2
• B. 16
• C. 4
• D. $\sqrt{2}$

Answer 1

The correct option is C 4

$4^{{\sqrt{x}}^{\sqrt{x}}}=256=4^4$
Equating powers with same bases:

$\Rightarrow {\sqrt{x}}^{\sqrt{x}}=4=2^2$

Since, ${\sqrt{x}}^{\sqrt{x}}=2^2$, we can take:

$\sqrt{x}=2\Rightarrow x=4$