Question

Expand log p square q cube by r​

Answer 1

$\textbf{Formula used:}$

$\textbf{Product rule:}$

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

$\textbf{Quotient rule:}$

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

$\textbf{Power rule:}$

$\boxed{\bf\,log_aM^n=n\;log_aM}$

$\textbf{To find:}$

$\text{Expansion of }\;log(\dfrac{p^2q^3}{r})$

$\textbf{Solution:}$

$\text{Consider,}$

$log(\dfrac{p^2q^3}{r})$

$\text{using quotient rule}$

$=log(p^2q^3)-log\,r$

$\text{using product rule}$

$=log\,p^2+log\,q^3-log\,r$

$\text{using power rule}$

$=2\,log\,p+3\,log\,q-log\,r$

$\therefore\bf\,log(\dfrac{p^2q^3}{r})=2\,log\,p+3\,log\,q-log\,r$

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