How do you use the properties of logarithms to expand lnsqrt(x^2(x+2))lnx2(x+2)?

1 Answer
Mar 9, 2017

see below

Explanation:

Use the following Properties of Logarithm

log_bx^n = nlog_b xlogbxn=nlogbx and log_b(xy)=log_bx+log_bylogb(xy)=logbx+logby

Hence,

ln sqrt(x^2(x+2))=ln(x^2(x+2))^(1/2lnx2(x+2)=ln(x2(x+2))12

=1/2* ln(x^2(x+2))=12ln(x2(x+2))

=1/2( lnx^2+ln(x+2))=12(lnx2+ln(x+2))

=1/2 (2lnx+ln(x+2))=12(2lnx+ln(x+2))

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