Question

Find $x$ if $\sqrt{2^{x+3}}=16$.

• A. 0
• B. 5
• C. 1
• D. 8

Answer 1

The correct option is B

5

Given $\sqrt{2^{x+3}}=16$

Squaring both sides, we get

$2^{x+3}={16}^2$ $[\because 16=2^4]$

${16}^2={\left(2^4\right)}^2=2^8$
$[\because {\left(a^m\right)}^n=a^{(m\times n)}]$

$\Rightarrow$ $2^{x+3}=2^8$

Since bases are equal, exponents should be equal.

$x+3=8$

$\Rightarrow x=8-3=5$