The value of `x` for which `((7)/(12)) ^(-4) xx ((7)/(12))^(3x) = ((7)/(12))^(5) ` is

Options

A. `-1`
B. 1
C. 2
D. 3

Answer

To solve the equation \(\left(\frac{7}{12}\right)^{-4} \times \left(\frac{7}{12}\right)^{3x} = \left(\frac{7}{12}\right)^{5}\), we can follow these steps:

### Step 1: Apply the property of exponents
We know that when multiplying two powers with the same base, we can add the exponents. Therefore, we can rewrite the left side of the equation as:
\[ \left(\frac{7}{12}\right)^{-4 + 3x} \]

### Step 2: Set the exponents equal
Since the bases are the same, we can set the exponents equal to each other:
\[ -4 + 3x = 5 \]

### Step 3: Solve for \(x\)
Now, we will isolate \(x\):
1. Add 4 to both sides:
\[ 3x = 5 + 4 \]
\[ 3x = 9 \]
2. Divide both sides by 3:
\[ x = \frac{9}{3} \]
\[ x = 3 \]

### Final Answer
The value of \(x\) is \(3\).

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