https://file.aiquickdraw.com/mathbot/file/172998929143643nsbomc.jpg

The equation provided in the image is:

\[
8^x = 2
\]

To solve for \(x\), we rewrite both sides using the same base. Notice that \(8\) can be expressed as a power of \(2\):

\[
8 = 2^3
\]

Thus, the equation becomes:

\[
(2^3)^x = 2
\]

Using the power rule \((a^m)^n = a^{m \cdot n}\), we get:

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

Since the bases are equal, we equate the exponents:

\[
3x = 1
\]

Now, solve for \(x\):

\[
x = \frac{1}{3}
\]

So, the solution is:

\[
x = \frac{1}{3}
\]

Would you like to explore further details, such as graphing this equation or confirming the solution step-by-step?

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**Related Questions:**
1. What happens to the solution if the base is different (e.g., \(4^x = 2\))?
2. How can logarithms help in solving equations like \(a^x = b\) when the bases differ?
3. What is the general solution for exponential equations of the form \(a^{kx} = c\)?
4. How can we solve the equation \(8^x = 10\) analytically or with a calculator?
5. What is the inverse function of the exponential function \(8^x\)?

**Tip:** When solving exponential equations, rewriting numbers with the same base simplifies the problem greatly!

What number x makes the equation 8^x = 2 correct?

Find the value of x that makes the equation 8^x = 2 correct. This solution involves understanding exponential equations, rewriting with the same base, and using exponent comparison. Suitable for students in Grades 8-10.

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