How do you expand #ln (e^3/(xy))#?

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Answer 1 · 2016-07-16T23:30:06

#ln(e^3/(xy))= -ln x - ln y + 3#

To expand, we can use the properties of logarithms.

The properties of logarithms are:

#ln(u*v) = ln(u) + ln(v)#

#ln(u/v) = ln(u) - ln(v)#

#ln(u^n) = n*ln(u)#

Also remember that #ln(e) = 1#.

Rewriting our expression yields

#ln(e^3/(xy)) = ln(e^3) - ln(xy)#

#= 3cancel(ln(e)) - [ln x + ln y]#

#=3 - ln x - ln y#

#= -ln x - ln y + 3#