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

1 Answer
Mar 9, 2017

Answer:

see below

Explanation:

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)#