Question

evaluate.

$\ln \frac { 1 } { e ^ { 17 } }$

$\ln \frac { 1 } { e ^ { 17 } } =$

Explanation:

Step1: Use the property of exponents

Recall that \(\frac{1}{a^b}=a^{-b}\). So, \(\frac{1}{e^{17}} = e^{- 17}\). Then the expression becomes \(\ln(e^{-17})\).

Step2: Use the property of logarithms

Recall the property \(\ln(a^b)=b\ln(a)\). For \(a = e\) and \(b=-17\), since \(\ln(e) = 1\), we have \(\ln(e^{-17})=-17\ln(e)\).

Step3: Simplify the expression

Substitute \(\ln(e) = 1\) into \(-17\ln(e)\). So, \(-17\ln(e)=-17\times1\).

Answer:

\(-17\)