Question

4.6
score: 5/12 answered: 5/12
question 5
let ( f(x)=3 ln x - 7 ).
evaluate ( f(e) ) to 4 decimal places.
( f(e)= )
question help: ebook written example

Explanation:

Step1: Substitute \(x = e\) into the function

Given \(f(x)=3\ln x - 7\), when \(x = e\), we have \(f(e)=3\ln(e)-7\).

Step2: Use the property of the natural logarithm

Since \(\ln(e) = 1\) (by the definition of the natural logarithm, \(\ln(a^b)=b\ln(a)\) and for \(a = e\), \(b = 1\), \(\ln(e^1)=1\times\ln(e)\) and \(y = \ln(x)\) is the inverse function of \(y = e^x\), so \(e^{\ln(e)}=e^1\) implies \(\ln(e)=1\)), then \(f(e)=3\times1 - 7\).

Step3: Calculate the value

\(f(e)=3 - 7=-4.0000\) (already to 4 decimal places as \(- 4=-4.0000\) in 4 - decimal - place form).

Answer:

\(-4.0000\)