If `(3/4)^3 (4/3)^(-7) = (3/4)^(2x)`,then x is :
यदि `(3/4)^3 (4/3)^(-7) =(3/4)^(2x)` हो, तो x कितना होगा?

Options

A. A)2
B. B)5
C. C)`2 1/2`
D. D)`-2`

Explanation

To solve the equation \((\frac{3}{4})^3 \cdot (\frac{4}{3})^{-7} = (\frac{3}{4})^{2x}\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the left-hand side of the equation:
\[ (\frac{3}{4})^3 \cdot (\frac{4}{3})^{-7} \]
We can rewrite \((\frac{4}{3})^{-7}\) as \((\frac{3}{4})^7\) because:
\[ (\frac{4}{3})^{-7} = \frac{1}{(\frac{4}{3})^7} = (\frac{3}{4})^7 \]

### Step 2: Combine the powers
Now substituting this back into the equation gives us:
\[ (\frac{3}{4})^3 \cdot (\frac{3}{4})^7 \]
Since the bases are the same, we can add the exponents:
\[ (\frac{3}{4})^{3 + 7} = (\frac{3}{4})^{10} \]

### Step 3: Set the equation
Now we have:
\[ (\frac{3}{4})^{10} = (\frac{3}{4})^{2x} \]

### Step 4: Compare the exponents
Since the bases are the same, we can set the exponents equal to each other:
\[ 10 = 2x \]

### Step 5: Solve for \(x\)
To find \(x\), divide both sides by 2:
\[ x = \frac{10}{2} = 5 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{5} \]