Question
Find $x$, if $: \sqrt{2^{x+3}}=16$
✓
Answer
$\sqrt{2^{x+3}}=16$
$ \left(2^{x+3}\right)^{\frac{1}{2}}=2 \times 2 \times 2 \times 2$
$ \Rightarrow(2)^{\frac{x+3}{2}}=2^4$
We know that if bases are equal, the powers are equal.
$\Rightarrow \frac{x+3}{2}=4$
$ \Rightarrow x+3=8$
$ \Rightarrow x=8-3$
$ \Rightarrow x=5$
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