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


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