We are asked to solve the equation $\ln(x) - \ln(9) = 10$ for $x$ and give the answer correct to 3 decimal places.

1. Problem Description

We are asked to solve the equation $\ln(x) - \ln(9) = 10$ for $x$ and give the answer correct to 3 decimal places.

2. Solution Steps

First, we use the property of logarithms that $\ln(a) - \ln(b) = \ln(\frac{a}{b})$ to rewrite the equation as:

$\ln(\frac{x}{9}) = 10$

Next, we exponentiate both sides of the equation using the base $e$ to remove the natural logarithm:

$e^{\ln(\frac{x}{9})} = e^{10}$

$\frac{x}{9} = e^{10}$

Now, we solve for $x$ by multiplying both sides by 9:

$x = 9e^{10}$

Finally, we approximate the value of $x$ to 3 decimal places.

$x \approx 9 \times 22026.46579$

$x \approx 198238.19211$

Rounding to three decimal places, we get $x \approx 198238.192$.

3. Final Answer

$x = 9e^{10} \approx 198238.192$