Find the value of 'x'. If `8^(x) xx 32^(x)=2^(10)`
(a)`1//8`
(b)`10//8`
(c)`20//8`
(d)`30//8`

Options

A. `1//8`
B. `10//8`
C. `20//8`
D. `30//8`

Answer

To solve the equation \( 8^x \times 32^x = 2^{10} \), we will first express the bases in terms of powers of 2.

### Step 1: Rewrite the bases
We know that:
- \( 8 = 2^3 \)
- \( 32 = 2^5 \)

Thus, we can rewrite the equation as:
\[ (2^3)^x \times (2^5)^x = 2^{10} \]

### Step 2: Simplify the equation
Using the power of a power property \((a^m)^n = a^{m \cdot n}\), we can simplify the left side:
\[ 2^{3x} \times 2^{5x} = 2^{10} \]

### Step 3: Combine the exponents
When multiplying powers with the same base, we add the exponents:
\[ 2^{3x + 5x} = 2^{10} \]
This simplifies to:
\[ 2^{8x} = 2^{10} \]

### Step 4: Set the exponents equal to each other
Since the bases are the same, we can set the exponents equal to each other:
\[ 8x = 10 \]

### Step 5: Solve for \(x\)
Now, we can solve for \(x\) by dividing both sides by 8:
\[ x = \frac{10}{8} = \frac{5}{4} \]

### Final Answer
Thus, the value of \(x\) is:
\[ \frac{5}{4} \]