How do you use the properties of logarithms to expand $lnsqrt(x^2(x+2))$ ?

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Answer 1 · 2017-03-09T20:09:39

see below

Use the following Properties of Logarithm

$log_bx^n = nlog_b x$ and $log_b(xy)=log_bx+log_by$

Hence,

$ln sqrt(x^2(x+2))=ln(x^2(x+2))^(1/2$

$=1/2* ln(x^2(x+2))$

$=1/2( lnx^2+ln(x+2))$

$=1/2 (2lnx+ln(x+2))$

$:.=lnx+1/2 ln(x+2)$

How do you use the properties of logarithms to expand lnsqrt(x^2(x+2))lnsqrt(x^2(x+2))?