Question

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

Answer 1

`\large\boxed{\ln\sqrt[3]{e^4}=(4)/(3)}`

Explanation:

`\text{Use}\\\\\sqrt[n]{a^m}=a^(m)/(n)\\\\\ln a^n=n\ln a\\\\\ln e=1\\-----------\\\\\ln\sqrt[3]{e^4}=\ln e^(4)/(3)=(4)/(3)\ln e=(4)/(3)\cdot1=(4)/(3)`