Question

Expand log120/49????????

Answer 1

$\textbf{Formula used:}$

$\textbf{Product rule:}$

$\boxed{\bf\,log_a(MN)=log_aM+log_aN}$

$\textbf{Qutient rule:}$

$\boxed{\bf\,log_a(\frac{M}{N})=log_aM-log_aN}$

$\text{Now,}$

$log(\frac{120}{49})$

$=log\,120-log\,49$ $\text{(Using quotient rule)}$

$=log\,(2{\times}2{\times}3{\times}5)-log\,(7{\times}7)$

$=log\,2+log\,2+log\,3+log\,5-[log\,7+log\,7]$ $\text{(Using product rule)}$

$=2\,log\,2+log\,3+log\,5-2\,log\,7$

$\therefore\bf\,log(\frac{120}{49})=2\,log\,2+log\,3+log\,5-2\,log\,7$

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Expand log 243 to the base 3 root 3

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