Solve each of the following exponential equations.
`6^(x-4) = 1`

Answer

To solve the exponential equation \( 6^{(x-4)} = 1 \), we can follow these steps:

### Step 1: Recognize that 1 can be expressed as an exponent
We know that any non-zero number raised to the power of 0 equals 1. Therefore, we can express 1 as:
\[ 1 = 6^0 \]

### Step 2: Set the exponents equal to each other
Since the bases are the same (both are 6), we can set the exponents equal to each other:
\[ x - 4 = 0 \]

### Step 3: Solve for \( x \)
Now, we can solve for \( x \) by adding 4 to both sides of the equation:
\[ x = 4 \]

### Final Answer
Thus, the solution to the equation \( 6^{(x-4)} = 1 \) is:
\[ \boxed{4} \]

---