Question

I'm having trouble with my algebra homework. Can you find the solution to the equation 2^(x+1) = 64 and show me the step-by-step process to solve it?

Answer 1

To solve the equation \( 2^{(x + 1)} = 64 \), we can follow these steps:

### Step 1: Rewrite 64 as a power of 2
First, we need to express 64 as a power of 2. We know that:
\[
64 = 2^6
\]
This allows us to rewrite the equation as:
\[
2^{(x + 1)} = 2^6
\]

### Step 2: Set the exponents equal to each other
Since the bases on both sides of the equation are the same (both are base 2), we can set the exponents equal to each other:
\[
x + 1 = 6
\]

### Step 3: Solve for \( x \)
To isolate \( x \), we subtract 1 from both sides of the equation:
\[
x = 6 - 1
\]
\[
x = 5
\]

### Conclusion
The solution to the equation \( 2^{(x + 1)} = 64 \) is:
\[
\boxed{5}
\]