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log(x) = 3 + log(y)

find x/y

 Apr 6, 2020
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\(\log_{10}(x) = 3 + \log_{10}(y)\)


find \(\dfrac{x}{y}\)

 

Formula:

\(\boxed{\log\left({\dfrac{x}{y}}\right) = \log(x)-\log(y)}\)

 

\(\begin{array}{|rcll|} \hline \log_{10}(x) &=& 3 + \log_{10}(y) \quad | \quad -\log_{10}(y) \\\\ \log_{10}(x) -\log_{10}(y) &=& 3 \\\\ \log_{10}\left({\dfrac{x}{y}}\right) &=& 3 \\\\ \dfrac{x}{y} &=& 10^3 \\\\ \mathbf{ \dfrac{x}{y} } &=& \mathbf{1000} \\ \hline \end{array}\)

 

laugh

 Apr 6, 2020

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