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 $a^((bc))=(a^b)^c$ :

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

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