How do you simplify e^(3lnx)?

2 Answers
Feb 25, 2016

${e}^{3 \ln x} = {x}^{3}$

Explanation:

Let ${e}^{3 \ln x} = k$, then $\ln k = 3 \ln x$.

But $3 \ln x = \ln \left({x}^{3}\right)$,

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

Hence, ${e}^{3 \ln x} = {x}^{3}$

Aug 10, 2016

${e}^{3 \ln x} = {x}^{3}$

Explanation:

Note that since ${a}^{{\log}_{a} b} = b$, we see that ${e}^{\ln} x = {e}^{{\log}_{e} x} = x$.

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

${e}^{3 \ln x} = {\left({e}^{\ln} x\right)}^{3} = {\left(x\right)}^{3} = {x}^{3}$