To solve this problem, we need to determine the value of x, which represents the value of the expression $\log_{10} (ML) + \log_{10} (MR)$.
Let's break down the information given:
$\log_{10} (AL) + \log_{10} (AM) = 2$
$\log_{10} (ML) + \log_{10} (MR) = X$
$\log_{10} (RA) + \log_{10} (RL) = 4$
We can use the properties of logarithms to simplify these equations.
From the first equation, we know that $\log_{10} (AL \cdot AM) = 2$. Using the property $\log_a (b \cdot c) = \log_a b + \log_a c$, we can rewrite this as $\log_{10} (AL) + \log_{10} (AM) = 2$.
Similarly, from the third equation, we know that $\log_{10} (RA \cdot RL) = 4$.
Now, let's substitute these simplified equations into the second equation:
$\log_{10} (ML) + \log_{10} (MR) = X$
$\log_{10} (RA \cdot RL) + \log_{10} (AL \cdot AM) = X$
Using the property $\log_a b + \log_a c = \log_a (b \cdot c)$, we can simplify this equation further:
$\log_{10} ((RA \cdot RL) \cdot (AL \cdot AM)) = X$
$\log_{10} (ARML^2) = X$
To solve for x, we need to find the value of $\log_{10} (ARML^2)$ which equals X. From the given information, we know that the value of $ARML^2$ is 1000. Therefore, the value of x is:
$\log_{10} (1000) = X$
$X = 3$
The value of x is 3.
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Let $A,$ $R,$ $M,$ and $L$ be positive real numbers such that
\begin{align*}
\log_{10} (AL) + \log_{10} (AM) &= 2, \\
\log_{10} (ML) + \log_{10} (MR) &= X, \\
\log_{10} (RA) + \log_{10} (RL) &= 4.
\end{align*}Compute the value of the product $ARML. The answer is 1000. What is the value of unknown variable X?

### Answer:
