How do you find the exact value of $ln \sqrt[4]{e^{3}}$ $lnroot4(e^3)$ ?

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Answer 1 · 2017-01-04T23:13:19

$\frac{3}{4}$ $3/4$

Use $\sqrt[n]{a^{m}} = a^{\frac{m}{n}}$ $root(n)(a^m) = a^(m/n)$ .

$= ln (e^{\frac{3}{4}})$ $=ln (e^(3/4))$

Use the rule ${ln a}^{n} = n ln a$ $lna^n = nlna$ :

$= \frac{3}{4} ln e$ $=3/4lne$

Since $y = ln x$ $y = lnx$ and $y = e^{x}$ $y = e^x$ are inverses, their product will be $1$ $1$ .

$= \frac{3}{4}$ $=3/4$

Hopefully this helps!

How do you find the exact value of lnroot4(e^3)ln4√e3lnroot4(e^3)?