$$ \partial ^ { x } - 2 ^ { x - 1 } = 2 $$

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UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$2^{x}-2^{x-1}=2$$
- step1: Subtract the terms:
  $$2^{x-1}=2$$
- step2: Set the exponents equal:
  $$x-1=1$$
- step3: Move the constant to the right side:
  $$x=1+1$$
- step4: Add the numbers:
  $$x=2$$
To solve the equation $$ 2^{x} - 2^{x-1} = 2 $$, we can follow these steps:

1. **Rewrite the equation**: The term $$ 2^{x-1} $$ can be rewritten as $$ \frac{2^{x}}{2} $$. Thus, the equation becomes:
   $$
   2^{x} - \frac{2^{x}}{2} = 2
   $$

2. **Combine like terms**: This simplifies to:
   $$
   2^{x} - \frac{1}{2} \cdot 2^{x} = 2
   $$
   Which can be factored as:
   $$
   \frac{1}{2} \cdot 2^{x} = 2
   $$

3. **Multiply both sides by 2**: To eliminate the fraction, we multiply both sides by 2:
   $$
   2^{x} = 4
   $$

4. **Express 4 as a power of 2**: We know that $$ 4 = 2^{2} $$, so we can set the exponents equal to each other:
   $$
   x = 2
   $$

Thus, the solution to the equation is:
$$
\boxed{2}
$$
The solution to the equation $$ 2^{x} - 2^{x-1} = 2 $$ is $$ x = 2 $$.

\( \partial ^ { x } - 2 ^ { x - 1 } = 2 \)

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