To solve the equation \(2^x = 8^x\), we can start by expressing \(8\) in terms of a base of \(2\):
\[ 8 = 2^3 \]
So we can rewrite \(8^x\) as:
\[ 8^x = (2^3)^x = 2^{3x} \]
Now we can substitute this back into the original equation:
\[ 2^x = 2^{3x} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x = 3x \]
Next, we can isolate \(x\) by subtracting \(3x\) from both sides:
\[ x - 3x = 0 \]
This simplifies to:
\[ -2x = 0 \]
Dividing both sides by \(-2\), we find:
\[ x = 0 \]
Thus, the solution to the equation \(2^x = 8^x\) is:
\[ \boxed{0} \]