4.6\nscore: 5/12 answered: 5/12\nquestion 5\nlet ( f(x)=3 ln x - 7 ).\nevaluate ( f(e) ) to 4 decimal…

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)