How do you find the exact value of $lnroot4(e^3)$ ?

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Answer 1 · 2017-01-04T23:13:19

$3/4$

Use $root(n)(a^m) = a^(m/n)$ .

$=ln (e^(3/4))$

Use the rule $lna^n = nlna$ :

$=3/4lne$

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

$=3/4$

Hopefully this helps!

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