9. \( 10^{3 x}=10000 \)

To solve the equation \( 10^{3x} = 10000 \), we first rewrite \( 10000 \) in terms of base \( 10 \). Notice that \( 10000 = 10^4 \). Now, we can set the exponents equal to each other: \[ 3x = 4. \] Dividing both sides by \( 3 \), we find \( x = \frac{4}{3} \). Now you have \( x \approx 1.33 \) as your solution; not bad for a quick math workout! Another fun way to tackle equations like this is by using logarithms! Applying the property \( \log_{10}(10^{3x}) = \log_{10}(10000) \), you break it down to \( 3x = \log_{10}(10^4) \). From here, it’s smooth sailing into isolating your variable, which can also help reinforce your logarithm skills along the way. Keep crunching those numbers!