Question

let ( f(x)=6 ln x - 3 ).
for what value of ( x ) will ( f(x)=5 )? answer exactly.
( x= )
question help: ( square ) ebook ( square ) written example

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:

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