If `289=17^(x/5)`, then x = ?

Options

A. 16
B. 2
C. 10
D. `2/5`

Answer

To solve the equation \( 289 = 17^{(x/5)} \), we can follow these steps:

### Step 1: Rewrite 289 as a power of 17
We know that \( 289 \) can be expressed as \( 17^2 \). Therefore, we can rewrite the equation as:
\[ 17^2 = 17^{(x/5)} \]

### Step 2: Set the exponents equal to each other
Since the bases are the same (both are 17), we can set the exponents equal to each other:
\[ 2 = \frac{x}{5} \]

### Step 3: Solve for \( x \)
To solve for \( x \), we can multiply both sides of the equation by 5:
\[ x = 2 \times 5 \]
\[ x = 10 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{10} \]

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