Question

The two functions f(x)=9e^x and g(x)=30 are graphed. Their intersection point is approximately (1.2,-30). What is the solution of the equation 9e^x=30 ? (1 point) x=□ Check answer Remaining Attempts : 3

Answer 1

To solve the equation \(9e^x = 30\), we start by isolating \(e^x\):

1. Divide both sides by 9:
\[
e^x = \frac{30}{9}
\]
Simplifying this gives:
\[
e^x = \frac{10}{3}
\]

2. Now, take the natural logarithm (ln) of both sides:
\[
\ln(e^x) = \ln\left(\frac{10}{3}\right)
\]
Using the property of logarithms \(\ln(e^x) = x\), we have:
\[
x = \ln\left(\frac{10}{3}\right)
\]

Now, we can calculate \( \ln\left(\frac{10}{3}\right) \) to find a numerical approximation:

\[
x \approx \ln(3.3333) \approx 1.20397,
\]
which rounds to approximately \(1.2\).

Thus, the solution to the equation \(9e^x = 30\) is:

\[
x \approx 1.2.
\]