The problem asks us to find the solution of the exponential equation $15e^x - 9 = 18$ in terms of logarithms or correct to four decimal places.

1. Problem Description

The problem asks us to find the solution of the exponential equation $15e^x - 9 = 18$ in terms of logarithms or correct to four decimal places.

2. Solution Steps

We are given the equation $15e^x - 9 = 18$.

First, we add 9 to both sides of the equation:

$15e^x = 18 + 9$

$15e^x = 27$

Next, we divide both sides by 15:

$e^x = \frac{27}{15}$

$e^x = \frac{9}{5}$

$e^x = 1.8$

Now, we take the natural logarithm of both sides:

$\ln(e^x) = \ln(1.8)$

$x = \ln(1.8)$

Using a calculator, we find the value of $\ln(1.8)$ to four decimal places:

$x \approx 0.5878$

3. Final Answer

$x = 0.5878$