Question

Solve for $x$ if $4^{{\sqrt{x}}^{\sqrt{x}}}=256$.

• A. $2$
• B. $16$
• C. $4$
• D. $\sqrt{2}$

Answer 1

Answer: (C)

$4$

$Now{4}^{{\sqrt{x}}^{\sqrt{x}}}=256$

$\to 4^{{\sqrt{x}}^{\sqrt{x}}}=4^4$

$Comparingpower,weget{\sqrt{x}}^{\sqrt{x}}=4$

$NowsubsitutingoptionsinLHS$

$A){\sqrt{x}}^{\sqrt{x}}={\sqrt{2}}^{\sqrt{2}}\ne RHS$

$B){\sqrt{x}}^{\sqrt{x}}={\sqrt{16}}^{\sqrt{16}}=4^4=256\ne RHS$

$C){\sqrt{x}}^{\sqrt{x}}={\sqrt{4}}^{\sqrt{4}}=2^2=4=RHS$

$D){\sqrt{x}}^{\sqrt{x}}={\sqrt{\sqrt{2}}}^{\sqrt{\sqrt{2}}}\ne RHS$

$\therefore valueofx=4$