iz $$ 2.5 \& 2.6 $$ Question 4 of 10 Solve the given equation for $$ x $$. $$ 2^{5-2 x}=2^{3 x-8} $$ $$ x= $$ $$ \square $$ (Type a fraction or an integer. Simplify your answer.)

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UpStudy AI · Accepted Answer

To solve the equation $$ 2^{5 - 2x} = 2^{3x - 8} $$ for $$ x $$, follow these steps:

1. **Since the bases are the same**, you can set the exponents equal to each other:
   $$
   5 - 2x = 3x - 8
   $$

2. **Combine like terms** by adding $$ 2x $$ to both sides:
   $$
   5 = 5x - 8
   $$

3. **Isolate the variable term** by adding $$ 8 $$ to both sides:
   $$
   13 = 5x
   $$

4. **Solve for $$ x $$** by dividing both sides by $$ 5 $$:
   $$
   x = \frac{13}{5}
   $$

**Final Answer:**
$$
x = \frac{13}{5}
$$
$$ x = \frac{13}{5} $$

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Question 4 of 10

Solve the given equation for .

(Type a fraction or an integer. Simplify your answer.)

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iz Question 4 of 10 Solve the given equation for . (Type a fraction or an integer. Simplify your answer.)