12. $$ 3^{10 x}=3^{2 x+6}=3^{2 x+6} $$ $$ 3^{10 x} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
3^{10x} = 3^{2x + 6}
$$

we can utilize the property of exponents that states if the bases are equal, then the exponents must be equal as well.

**Step 1: Set the exponents equal to each other**

Since the base $$3$$ is the same on both sides of the equation, we can equate the exponents:

$$
10x = 2x + 6
$$

**Step 2: Solve for $$x$$**

Subtract $$2x$$ from both sides to isolate the terms containing $$x$$:

$$
10x - 2x = 6
$$

$$
8x = 6
$$

Now, divide both sides by $$8$$ to solve for $$x$$:

$$
x = \frac{6}{8}
$$

Simplify the fraction:

$$
x = \frac{3}{4}
$$

**Solution:**

$$
x = \frac{3}{4}
$$
$$ x = \frac{3}{4} $$

12. \( 3^{10 x}=3^{2 x+6}=3^{2 x+6} \) \( 3^{10 x} \)