How do you simplify $e^{3 ln x}$ $e^(3lnx)$ ?

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Answer 1 · 2016-02-25T12:49:32

$e^{3 ln x} = x^{3}$ $e^(3lnx)= x^3$

Let $e^{3 ln x} = k$ $e^(3lnx)=k$ , then $ln k = 3 ln x$ $lnk=3lnx$ .

But $3 ln x = ln (x^{3})$ $3lnx=ln(x^3)$ ,

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

Hence, $e^{3 ln x} = x^{3}$ $e^(3lnx)=x^3$

Answer 2 · 2016-08-10T03:05:31

$e^{3 ln x} = x^{3}$ $e^(3lnx)=x^3$

Note that since $a^{{log}_{a} b} = b$ $a^(log_ab)=b$ , we see that $e^{ln x} = e^{{log}_{e} x} = x$ $e^lnx=e^(log_ex)=x$ .

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

$e^{3 ln x} = {(e^{ln x})}^{3} = {(x)}^{3} = x^{3}$ $e^(3lnx)=(e^lnx)^3=(x)^3=x^3$

How do you simplify e3lnxe^(3lnx)?