Question

let ( f(x)=7ln x - 4 ).
evaluate ( f(e) ) to 4 decimal places.
( f(e)=)
question help: ( square ) ebook ( square ) written example

Explanation:

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

Given \(f(x)=7\ln x - 4\), when \(x = e\), we have \(f(e)=7\ln(e)-4\).

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 \(a = e\), \(b = 1\), \(y=\ln(e)\) is equivalent to \(e^y=e^1\)), then \(f(e)=7\times1 - 4\).

Step3: Calculate the result

\(f(e)=7 - 4=3.0000\) (rounded to 4 decimal places)

Answer:

\(3.0000\)