The problem is to solve the equation $\ln(x) + \ln(6) = 3$ for $x$ and give the answer correct to 3 decimal places.

1. Problem Description

The problem is to solve the equation $\ln(x) + \ln(6) = 3$ for $x$ and give the answer correct to 3 decimal places.

2. Solution Steps

We are given the equation $\ln(x) + \ln(6) = 3$.

Using the logarithm property $\ln(a) + \ln(b) = \ln(ab)$, we can rewrite the equation as:

$\ln(6x) = 3$

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

$e^{\ln(6x)} = e^3$

Since $e^{\ln(y)} = y$, we have:

$6x = e^3$

Now, we can solve for $x$ by dividing both sides by 6:

$x = \frac{e^3}{6}$

We can approximate $e^3$ as $20.0855$ and then divide by 6:

$x = \frac{20.0855}{6} \approx 3.34758333...$

Rounding the result to 3 decimal places, we get $x \approx 3.348$.

3. Final Answer

$x = 3.348$