Write the following expressions as a single logarithm. (x+2)+ (x-… - Vidyadip

Question

Write the following expressions as a single logarithm.$\ln (x+2)+\ln (x-2)-3 \ln (x+5)$

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Answer

$\ln (x+2)+\ln (x-2)-3 \ln (x+5)$
$=\ln [(x+2)(x-2)]-\ln (x+5)^3$
$\ldots\left[\begin{array}{l} \log m+\log n=\log m n \\ n \log m=\log m^n \end{array}\right]$
$=\ln \left(x^2-4\right)-\ln (x+5)^3$
$=\ln \left(\frac{x^2-4}{(x+5)^3}\right) \ldots\left[\log m-\operatorname{logn}=\log \frac{m}{n}\right]$

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