Solve the following for $$ x $$ 1. $$ 2^{x+1}-2^{x}=8 $$

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To solve the equation $$ 2^{x+1} - 2^{x} = 8 $$ for $$ x $$, follow these steps:

1. **Simplify the Left Side:**
   
   Recall that $$ 2^{x+1} = 2 \cdot 2^{x} $$. Substitute this into the equation:
   
   $$
   2 \cdot 2^{x} - 2^{x} = 8
   $$

2. **Factor Out $$ 2^{x} $$:**
   
   Factor $$ 2^{x} $$ from the left side:
   
   $$
   (2 - 1) \cdot 2^{x} = 8
   $$
   
   Simplify:
   
   $$
   1 \cdot 2^{x} = 8 \quad \Rightarrow \quad 2^{x} = 8
   $$

3. **Solve for $$ x $$:**
   
   Recognize that $$ 8 $$ is a power of $$ 2 $$:
   
   $$
   8 = 2^{3}
   $$
   
   Therefore:
   
   $$
   2^{x} = 2^{3} \quad \Rightarrow \quad x = 3
   $$

**Final Answer:** $$ x = 3 $$
$$ x = 3 $$

Solve the following for \( x \) 1. \( 2^{x+1}-2^{x}=8 \)

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