To solve the equation \( 4^{x+1} = 64 \), let's follow these steps:

### Step 1: Express 64 as a power of 4
We know that \( 64 = 4^3 \), because \( 4^3 = 4 \times 4 \times 4 = 64 \).

### Step 2: Rewrite the equation
Now the equation becomes:
\[
4^{x+1} = 4^3
\]

### Step 3: Equate the exponents
Since the bases are the same, we can set the exponents equal to each other:
\[
x + 1 = 3
\]

### Step 4: Solve for \( x \)
Subtract 1 from both sides:
\[
x = 3 - 1
\]
\[
x = 2
\]

So, the solution is \( x = 2 \).

Would you like more details on any part of this solution? 

Here are 5 related questions for practice:
1. Solve \( 3^{x+2} = 27 \).
2. Solve \( 2^{2x+3} = 32 \).
3. If \( 5^{x-1} = 25 \), what is \( x \)?
4. Solve \( 9^{x+1} = 81 \).
5. Solve \( 8^{x+1} = 64 \).

**Tip:** When solving exponential equations, always try to express both sides as powers of the same base!

Learn how to solve the exponential equation 4^{x+1} = 64 by equating powers of the same base. This step-by-step solution covers key concepts in exponents and algebra, suitable for students in Grades 8-10.

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