How do you expand #ln (sqrt(ex^2)/y^3)#?

1 Answer
Jul 6, 2016

Answer:

#1/2+lnx-3lny#

Explanation:

Expanding this expression is done by applying two properties of #ln#
Quotient property:
#ln (a/b)=lna-lnb#

Product property:
#ln (a*b)=lna+lnb#

#Ln ((sqrt (ex^2))/y^3)#
#=ln (sqrt (ex^2 ))-ln (y^3)#
#=ln((ex^2)^(1/2))-3lny#
#=1/2ln (ex^2)-3lny#
#=1/2 (lne+ln (x^2))-3lny#
#=1/2 (1+2lnx)-3lny#
#=1/2+lnx-3lny#