Answer
$8.3$
Work Step by Step
As per the given problem, the magnitude of an earthquake $=log_{10}(\frac{I}{S})$
Where, I is the intensity of the quake (measured by the amplitude of a seismograph 100 km from the epicenter) and S is the intensity of a “standard” earthquake (where the amplitude is only 1 micron=$10^{-4}$ cm)
The magnitude of earthquake on the Richter scale in year 1989 = 7.1
Therefore,
$log_{10}(\frac{I}{S})=7.1$
The intensity of earthquake was 16 times as intense in the year of 1906. Therefore, the magnitude of earthquake $=log_{10}(\frac{16I}{S})$
Now,
$log_{10}(\frac{16I}{S})=log_{10}16+log_{10}(\frac{1}{S})$
$log_{10}(\frac{16I}{S})=log_{10}16+7.1$
Hence,
$log_{10}(\frac{16I}{S})= 8.3$
