If $r$ and $s$ are positive integers such that $\left(2^{r}\right)\left(4^{s}\right)=16$, then $2 r+s=$

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If r and s are positive integers such that (2^{r}) (4^{s}) = 16, then 2 r + s =

Explanation	Calculations	Help
$We rewrite 4 as a power of 2 and note that 16 is a power of 2.$	$4 = 2^{2} 16 = 2^{4}$	Theory & Tactics Method Card ALG7 Click to view full details
$We express the left-hand side entirely as a power of 2.$	$(2^{r}) (4^{s}) = 2^{r} (2^{2})^{s} = 2^{r + 2 s} 2^{r + 2 s} = 2^{4}$	Theory & Tactics Method Card ALG7 Click to view full details
$We match the exponents to get a linear equation and find the positive integer solutions, then compute the desired expression.$	$r + 2 s = 4 s = 1, r = 2 2 r + s = 2 \times 2 + 1 = 5$

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5

If r and s are positive integers such that (2^{r}) (4^{s}) = 16, then 2 r + s =

Explanation	Calculations	Help
$We rewrite 4 as a power of 2 and note that 16 is a power of 2.$	$4 = 2^{2} 16 = 2^{4}$	Theory & Tactics Method Card ALG7 Click to view full details
$We express the left-hand side entirely as a power of 2.$	$(2^{r}) (4^{s}) = 2^{r} (2^{2})^{s} = 2^{r + 2 s} 2^{r + 2 s} = 2^{4}$	Theory & Tactics Method Card ALG7 Click to view full details
$We match the exponents to get a linear equation and find the positive integer solutions, then compute the desired expression.$	$r + 2 s = 4 s = 1, r = 2 2 r + s = 2 \times 2 + 1 = 5$

Scroll horizontally to view all columns

5