Solve the equation.
2 Superscript 2 x plus 1 Baseline equals 8
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Part 1
The solution set is StartSet nothing EndSet
  
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​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)

The given equation is:

\[ 2^{2x + 1} = 8 \]

We can solve this step-by-step.

1. Rewrite 8 as a power of 2:

\[ 8 = 2^3 \]

So, the equation becomes:

\[ 2^{2x + 1} = 2^3 \]

2. Since the bases are the same, we can set the exponents equal to each other:

\[ 2x + 1 = 3 \]

3. Solve for \( x \):

\[ 2x + 1 = 3 \]
\[ 2x = 3 - 1 \]
\[ 2x = 2 \]
\[ x = \frac{2}{2} \]
\[ x = 1 \]

Therefore, the solution set is:

\[ \{ 1 \} \]

Do you want more details or have any questions?

Here are 5 numbered questions you can ask:
1. How do I solve quadratic equations?
2. Can you explain the Pythagorean theorem?
3. What are the properties of logarithms?
4. How do I find the derivative of a function?
5. Can you help me with solving systems of linear equations?

**Tip:** When solving equations involving exponents, try to express all terms with the same base to simplify the process.

Learn how to solve the equation 2^(2x + 1) = 8 with a detailed step-by-step solution. This problem covers exponential equations and the power of a base concept. Suitable for students in Grades 9-12.

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