If `3^(2x - 3) xx 5^(4x - 1) = 5^(2x + 1) xx 3^(4x - 5)`, then x =

Options

A. `-1`
B. 2
C. 1
D. `-2`

Answer

To solve the equation \(3^{(2x - 3)} \times 5^{(4x - 1)} = 5^{(2x + 1)} \times 3^{(4x - 5)}\), we can follow these steps:

### Step 1: Rewrite the equation
We start with the original equation:
\[ 3^{(2x - 3)} \times 5^{(4x - 1)} = 5^{(2x + 1)} \times 3^{(4x - 5)} \]

### Step 2: Rearrange the equation
We can rearrange the equation to group the terms with the same base:
\[ \frac{3^{(2x - 3)}}{3^{(4x - 5)}} = \frac{5^{(2x + 1)}}{5^{(4x - 1)}} \]

### Step 3: Simplify the fractions
Using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify both sides:
\[ 3^{(2x - 3) - (4x - 5)} = 5^{(2x + 1) - (4x - 1)} \]

### Step 4: Simplify the exponents
Now simplify the exponents:
- For the left side:
\[ (2x - 3) - (4x - 5) = 2x - 3 - 4x + 5 = -2x + 2 \]
- For the right side:
\[ (2x + 1) - (4x - 1) = 2x + 1 - 4x + 1 = -2x + 2 \]

So we have:
\[ 3^{-2x + 2} = 5^{-2x + 2} \]

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

### Step 6: Solve for \(x\)
Now, solve for \(x\):
\[ -2x = -2 \]
\[ x = 1 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{1} \]