Solve `12^(x) = 144` and find the value of `x`.

Answer

To solve the equation \( 12^x = 144 \) and find the value of \( x \), we can follow these steps:

### Step 1: Rewrite 144 in terms of base 12
We know that \( 144 \) can be expressed as \( 12 \times 12 \). Therefore, we can write:
\[ 144 = 12^2 \]

### Step 2: Substitute into the equation
Now, we can substitute \( 144 \) in the original equation:
\[ 12^x = 12^2 \]

### Step 3: Equate the exponents
Since the bases on both sides of the equation are the same (both are base 12), we can equate the exponents:
\[ x = 2 \]

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{2} \]

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