How do you expand #ln sqrt(m^2/(m+3))#?

1 Answer
Apr 6, 2018

Answer:

#color(blue)(ln(m)-1/2ln(m+3)#

Explanation:

#sqrt(m^2/(m+3))=(m^2/(m+3))^(1/2)#

#ln(m^2/(m+3))^(1/2)=1/2ln(m^2/(m+3))#

#ln(a/b)=ln(a)-ln(b)#

#1/2ln(m^2/(m+3))=1/2[ln(m^2)-ln(m+3)]#

# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =1/2[2ln(m)-ln(m+3)]#

# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =color(blue)(ln(m)-1/2ln(m+3))#