Question
Express the following in a form free from logarithm:$3 \log x - 2 \log y = 2$
✓
Answer
$3 \log x-2 \log y=2 $
$\Rightarrow \log x^3-\log y^2 $
$=2 \log 10$
$ \Rightarrow \log \left(\frac{x^3}{y^2}\right)=\log 10^2 $
$=\log 100$
$\Rightarrow\left(\frac{x^3}{y^2}\right)=100 $
$ \Rightarrow x^3=100 y^2$
$\Rightarrow \log x^3-\log y^2 $
$=2 \log 10$
$ \Rightarrow \log \left(\frac{x^3}{y^2}\right)=\log 10^2 $
$=\log 100$
$\Rightarrow\left(\frac{x^3}{y^2}\right)=100 $
$ \Rightarrow x^3=100 y^2$
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