let ( f(x)=7ln x - 4 ).\nevaluate ( f(e) ) to 4 decimal places.\n( f(e)=)\nquestion help: ( square ) ebook (…

let ( f(x)=7ln x - 4 ).\nevaluate ( f(e) ) to 4 decimal places.\n( f(e)=)\nquestion help: ( square ) ebook ( square ) written example

let ( f(x)=7ln x - 4 ).\nevaluate ( f(e) ) to 4 decimal places.\n( f(e)=)\nquestion help: ( square ) ebook ( square ) written example

Answer

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)