$$ 2^x= 7, 2^y = 14 $$
$$ \frac{2^x}{2^y} = \frac{7}{14} $$
$$ 2^{x-y} = \frac{1}{2} $$
$$ 2^{x-y} = 2^{-1} $$
$$ x-y = \boxed{-1} $$
Use the calculator to manually calculate \(x\) and \(y\). You can do this by changing it into logarithmic form, such as
$$ 2^x=7 $$
$$ \log_22^x = \log_27 $$
$$ x = \log_27 $$
After obtaining \(x\) and \(y\) with your calculator, just subtract them.
Technically, you can manually get the answer if you know logarithm rules:
$$ 2^y=14 $$
$$ \log_22^y = \log_214 $$
$$ y=\log_214 $$
$$ x-y = \log_27 -\log_214 $$
$$ = \log_2\left(\frac{7}{14}\right) $$
$$ = \log_2\left(\frac{1}{2}\right) $$
$$ = \log_2(2^{-1}) $$
$$ = -1\log_22$$
$$ = \boxed{-1} $$