So we need to solve the equation \(\pi^x=10^9.\) In order to solve for \(x\), we just need one simple step: take \(\log_{\pi}\) of both sides. This means that

$$\log_{\pi}\pi^x=\log_{\pi}10^9\implies x=\log_{\pi}10^9\approx 18.1.
$$

This however, cannot be done with a calculator. (A calculator only has log and log base \(e\).)