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)#