Question

Evaluate each logarithm. Do not use a calculator. ln ^3 square root e^4

Answer 1

Answer:

$\large\boxed{\ln\sqrt[3]{e^4}=\dfrac{4}{3}}$

Step-by-step explanation:

$\text{Use}\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\ln a^n=n\ln a\\\\\ln e=1\\-----------\\\\\ln\sqrt[3]{e^4}=\ln e^\frac{4}{3}=\dfrac{4}{3}\ln e=\dfrac{4}{3}\cdot1=\dfrac{4}{3}$