$$ 9^{x} imes 9^{2}=9^{12} $$ Find the value of $$ x $$

Question

$$ 9^{x} 	imes 9^{2}=9^{12} $$ Find the value of $$ x $$

UpStudy AI · Accepted Answer

To solve the equation:

$$
9^{x} \times 9^{2} = 9^{12}
$$

we can use the **laws of exponents**. Specifically, the **Product of Powers Property**, which states:

$$
a^{m} \times a^{n} = a^{m+n}
$$

### Step-by-Step Solution:

1. **Apply the Product of Powers Property:**

$$
   9^{x} \times 9^{2} = 9^{x + 2}
   $$

So the equation becomes:

$$
   9^{x + 2} = 9^{12}
   $$

2. **Since the bases are the same, set the exponents equal to each other:**

$$
   x + 2 = 12
   $$

3. **Solve for $$ x $$:**

$$
   x = 12 - 2
   $$
   
   $$
   x = 10
   $$

### **Answer:**
$$ x = 10 $$
$$ x = 10 $$

\( 9^{x} \times 9^{2}=9^{12} \) Find the value of \( x \)