If `3^(4X-2)=729`, then find the value of X.

Options

A. 4
B. 3
C. 2
D. 5

Answer

To solve the equation \( 3^{4X-2} = 729 \), we can follow these steps:

### Step 1: Rewrite 729 as a power of 3
We know that \( 729 \) can be expressed as a power of \( 3 \). Specifically, we can find that:
\[ 729 = 3^6 \]

### Step 2: Set the exponents equal to each other
Since the bases are the same, we can equate the exponents:
\[ 4X - 2 = 6 \]

### Step 3: Solve for X
Now, we will solve for \( X \):
1. Add \( 2 \) to both sides:
\[ 4X = 6 + 2 \]
\[ 4X = 8 \]
2. Divide both sides by \( 4 \):
\[ X = \frac{8}{4} \]
\[ X = 2 \]

### Final Answer
Thus, the value of \( X \) is \( 2 \).

---