Write the following expressions as sum or difference of logarithm… - Vidyadip

Question

Write the following expressions as sum or difference of logarithms:$\ln \left(\frac{a^3(a-2)^2}{\sqrt{b^2+5}}\right)$

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Answer

$ \ln \left(\frac{a^3(a-2)^2}{\sqrt{b^2+5}}\right)$
$=\ln \left(a^3(a-2)^2\right)-\ln \sqrt{b^2+5}$
$\quad \ldots\left[\log \frac{m}{n}=\log m-\log n\right]$
$ =\ln a^3+\ln (a-2)^2-\ln \left(b^2+5\right)^{\frac{1}{2}}$
$\qquad \ldots[\log m n=\log m+\log n]$
$=3 \ln a+2 \ln (a-2)-\frac{1}{2} \ln \left(b^2+5\right) $
$\ldots\left[\log m^n=n \log m\right]$

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