How do you condense #ln x + ln (x-2) - 5 ln y#?

1 Answer
Jun 22, 2016

Answer:

Use a few properties of logs to condense #lnx+ln(x-2)-5lny# into #ln((x^2-2x)/(y^5))#.

Explanation:

Begin by using the property #lna+lnb=lnab# on the first two logs:
#lnx+ln(x-2)=ln(x(x-2))=ln(x^2-2x)#

Now use the property #alnb=lnb^a# on the last log:
#5lny=lny^5#

Now we have:
#ln(x^2-2x)-lny^5#

Finish by combining these two using the property #lna-lnb=ln(a/b)#:
#ln(x^2-2x)-lny^5=ln((x^2-2x)/(y^5))#