let ( f(x)=8 ln x - 4 ).\nevaluate ( f(e) ) to 4 decimal places.\n( f(e)= )
let ( f(x)=8 ln x - 4 ).\nevaluate ( f(e) ) to 4 decimal places.\n( f(e)= )
Answer
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). [ \begin{align*} f(e)&=8 - 4\ &=4.0000 \end{align*} ]
Answer:
(4.0000)