Question

module 6 quiz (24-28)
100 points possible answered: 4/20
question 6
review: solve the equation. leave answer in exact form.
-2 + ln 3x = 7
x =
\frac{e^{9}}{3}
next question

Explanation:

Step1: Isolate the logarithmic term

Add 2 to both sides of the equation \(-2 + \ln 3x = 7\) to get \(\ln 3x = 7 + 2\).
Simplifying the right side gives \(\ln 3x = 9\).

Step2: Convert from logarithmic to exponential form

Recall that if \(\ln a = b\), then \(a = e^b\). So for \(\ln 3x = 9\), we have \(3x = e^9\).

Step3: Solve for x

Divide both sides of the equation \(3x = e^9\) by 3 to isolate x.
This gives \(x=\frac{e^9}{3}\).

Answer:

\(x = \frac{e^{9}}{3}\)