If ` 5^(5 x + 5) = 1 `, then x equals

Options

A. 0
B. `-1`
C. 1
D. `-(4)/(5)`

Answer

To solve the equation \( 5^{(5x + 5)} = 1 \), we can follow these steps:

### Step 1: Rewrite 1 as a power of 5
We know that any number raised to the power of 0 equals 1. Therefore, we can express 1 as:
\[ 1 = 5^0 \]

### Step 2: Set the exponents equal to each other
Since the bases are the same (both are 5), we can set the exponents equal to each other:
\[ 5x + 5 = 0 \]

### Step 3: Solve for \( x \)
Now, we need to isolate \( x \). Start by subtracting 5 from both sides:
\[ 5x = -5 \]
Next, divide both sides by 5:
\[ x = -1 \]

### Conclusion
Thus, the solution to the equation \( 5^{(5x + 5)} = 1 \) is:
\[ x = -1 \]

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