How do you simplify e^(3lnx)?

2 Answers
Feb 25, 2016

e^(3lnx)= x^3

Explanation:

Let e^(3lnx)=k, then lnk=3lnx.

But 3lnx=ln(x^3),

therefore lnk=ln(x^3), i.e. k=x^3

Hence, e^(3lnx)=x^3

Aug 10, 2016

e^(3lnx)=x^3

Explanation:

Note that since a^(log_ab)=b, we see that e^lnx=e^(log_ex)=x.

We will also use the rule that a^((bc))=(a^b)^c:

e^(3lnx)=(e^lnx)^3=(x)^3=x^3