To solve for the power of 10 in the equation \(7.34 \times 10^x = 0.000734\), we first need to express \(0.000734\) in terms of a power of 10.
We can rewrite \(0.000734\) as follows:
\[ 0.000734 = 7.34 \times 10^{-4} \]
Now we can substitute this back into the equation:
\[ 7.34 \times 10^x = 7.34 \times 10^{-4} \]
Since both sides have \(7.34\), we can divide both sides by \(7.34\):
\[ 10^x = 10^{-4} \]
This implies that:
\[ x = -4 \]
Thus, the value of \(x\) that makes the equation true is:
\[ \boxed{-4} \]