How do you simplify ln(1/e)^6-4tln(1e)64t?

2 Answers
Dec 1, 2015

-6-4t64t

Explanation:

ln(1/e)^6-4t=lne^-6-4tln(1e)64t=lne64t
=-6lne-4t=6lne4t
=-6-4t=64t

Dec 1, 2015

-2(3+2t)2(3+2t)

Explanation:

First of all, we have that log(x^a)=alog(x)log(xa)=alog(x). And since 1/e=e^{-1}1e=e1, we have that

ln(1/e)^6 = ln(e^-6)ln(1e)6=ln(e6)

So, ln(e^{-6}) = -6ln(e)ln(e6)=6ln(e)

And by definition, ln(e)=1ln(e)=1

So, the expression becomes -6-4t=-2(3+2t)64t=2(3+2t)