Question

sa se verifice:
$\frac{ log_{2}45 - log_{2}5 }{ log_{2}3 } = 2$
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Answer 1

 

$\displaystyle\bf\\\frac{ log_{2}45 - log_{2}5 }{ log_{2}3 }=\frac{ log_{2}\dfrac{45}{5}}{ log_{2}3 }=\frac{ log_{2}9}{log_{2}3}=\frac{ log_{2}3^2}{log_{2}3}=\frac{ 2\times log_{2}3}{log_{2}3}=2\\\\\\Se~simplifica~fractia~cu~~log_{2}3~~si~ramane~2.$