How much must the power output of a transmitter be raised to change the S meter reading on a distant receiver from S8 to S9?

Explanation

Moving one S unit means raising the received signal by 6 dB, and a 6 dB power increase is a ratio of 10^6/10 = 3.98, that is approximately four times. Since path loss is fixed, the transmitter power must be raised by that same factor of about four.