How do you simplify #e^(3lnx)#?

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Answer 1 · 2016-02-25T12:49:32

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

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#

Answer 2 · 2016-08-10T03:05:31

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

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#