Question
Solve for $x : \frac{\log 289}{\log 17}=\log x$
✓
Answer
$\frac{\log 289}{\log 17}=\log x $
$\Rightarrow \frac{\log 17^2}{\log 17}=\log x$
$ \Rightarrow \frac{2 \log 17}{\log 17}=\log x$
$ \Rightarrow 2=\log x $
$\Rightarrow 2 \log 10=\log x \ldots($ since $\log 10=1) $
$ \Rightarrow \log 10^2=\log x $
$\therefore x=10^2 $
$=100 .$
$\Rightarrow \frac{\log 17^2}{\log 17}=\log x$
$ \Rightarrow \frac{2 \log 17}{\log 17}=\log x$
$ \Rightarrow 2=\log x $
$\Rightarrow 2 \log 10=\log x \ldots($ since $\log 10=1) $
$ \Rightarrow \log 10^2=\log x $
$\therefore x=10^2 $
$=100 .$
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