let ( f(x)=6 ln x - 3 ).\nfor what value of ( x ) will ( f(x)=5 )? answer exactly.\n( x= )\nquestion help: (…

Explanation:

Step1: Set up the equation

Given ( f(x)=6\ln x - 3) and ( f(x) = 5), we set up the equation (6\ln x-3 = 5).

Step2: Solve for (\ln x)

Add (3) to both sides of the equation: (6\ln x=5 + 3), so (6\ln x=8). Then divide both sides by (6): (\ln x=\frac{8}{6}=\frac{4}{3}).

Step3: Solve for (x)

Using the property that if (\ln x = a), then (x = e^{a}). Here (a=\frac{4}{3}), so (x = e^{\frac{4}{3}}).

Answer:

(e^{\frac{4}{3}})