The equation provided is:

$\ln(x) - \ln(4) = 0$

To solve for $x$:

Step 1: Simplify the equation

Using the logarithmic property $\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)$, the equation becomes: $\ln\left(\frac{x}{4}\right) = 0$

Step 2: Exponentiate to eliminate the logarithm

Exponentiate both sides of the equation with base $e$: $\frac{x}{4} = e^0$ Since $e^0 = 1$: $\frac{x}{4} = 1$

Step 3: Solve for $x$

Multiply both sides by 4: $x = 4$

Final Answer:

$x = 4$

Would you like me to explain any step in more detail or provide additional related problems to practice? Here are some related questions to expand your understanding:

1. What is the general property of logarithms for subtraction, and how does it apply to different bases?
2. How would the solution change if the equation were $\ln(x) - \ln(a) = 0$ for some arbitrary $a$?
3. Can logarithmic equations like this have no solution or multiple solutions? Why or why not?
4. How would you graph $\ln(x) - \ln(4)$ and verify the solution visually?
5. What happens if you replace $\ln$ with $\log$ (logarithm base 10) in the equation?

Tip: Always check the domain of the logarithmic functions to ensure the arguments are valid (positive numbers).