Evaluate the following logarithmic expression without the use of a calculator. Enter your answer as a fraction reduced to the lowest terms. ln(\sqrt[7]{e4})

Question

Evaluate the following logarithmic expression without the use of a calculator. Enter your answer as a fraction reduced to the lowest terms. ln(
`\sqrt[7]{e4}`)

Answer 1

assuming you meant e⁴ thus



`\bf ln\left( \sqrt[7]{e^4} \right)\implies log_e\left( e^{(4)/(7)} \right)\\\\ -----------------------------\\\\ log_{{ a}}{{ a}}^x\implies x=x\impliedby \textit{let's use this cancellation rule}\\\\ -----------------------------\\\\ log_e\left( e^{(4)/(7)} \right)\iff \cfrac{4}{7}`