<s>[INST] If $47^x = 8$ and $376^y = 128$ , find $\frac{3}{x}-\frac{7}{y}$ What I know:
$x={\log_{47}8}$ and $y=\log_{376}128$
How do I do this without using a calculator?
 [/INST] No logs, no calculator.  :)
$$47^x=8=2^3\Longrightarrow 47=2^{3/x}\\
376^y=128=2^7\Longrightarrow 376=2^{7/y}$$
Dividing, 
$$\frac {2^{3/x}} {2^{7/y}}=\frac {47}{376}=\frac 18\\
2^{3/x-7/y}=2^{-3}\\
\frac 3x-\frac 7y=\color{red}{-3}$$
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