Question

let ( f(x)=8 ln x - 4 ).
evaluate ( f(e) ) to 4 decimal places.
( f(e)= )

Explanation:

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

Given \(f(x)=8\ln x - 4\), when \(x = e\), we know that \(\ln e=1\) (by the property of the natural logarithm, \(\ln a^b=b\ln a\) and for \(a = e\), \(b = 1\), \(e^1=e\), so \(\ln e = 1\)). Then \(f(e)=8\ln e-4\).

Step2: Calculate the value

Substitute \(\ln e = 1\) into the expression \(f(e)=8\ln e - 4\). We get \(f(e)=8\times1 - 4\).

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Answer:

\(4.0000\)