To solve the equation \(8^x = 2\), we can express both sides with the same base:

1. Rewrite 8 as a power of 2:
   \[
   8 = 2^3
   \]
   So, the equation becomes:
   \[
   (2^3)^x = 2
   \]

2. Apply the power of a power rule \( (a^m)^n = a^{mn} \):
   \[
   2^{3x} = 2^1
   \]

3. Since the bases are the same, you can set the exponents equal to each other:
   \[
   3x = 1
   \]

4. Solve for \(x\):
   \[
   x = \frac{1}{3}
   \]

Thus, the solution is \( x = \frac{1}{3} \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How would you solve \( 4^x = 16 \)?
2. Can you solve \( 27^x = 9 \) using similar steps?
3. What is the solution to \( 5^{2x} = 125 \)?
4. How do you solve \( 3^{x+2} = 27 \)?
5. What is the value of \( x \) in the equation \( 10^x = 0.01 \)?

**Tip:** When solving exponential equations, try to express both sides with the same base to simplify the problem.

Learn how to solve the exponential equation 8^x = 2 with a detailed step-by-step solution. This problem involves applying the power of a power rule to simplify the equation. Suitable for students in Grades 9-12.

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