Problema Solution
The magnitude of an earthquake, "R" is defined by "R" = log_(10)["I_c/I_n"] where "I_c" is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the earthquake) and "I_n" is the intensity of a ''standard earthquake'' (whose amplitude is 1 micron =10^-4 cm).
The 1906 San Francisco earthquake had a magnitude of 8.3 on the Richter scale. At the same time in South America there was an earthquake with magnitude 4.9 that caused only minor damage. How many times more intense was the San Francisco earthquake than the South American one?
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"R" = log_(10)["I_c/I_n"]
log_(10)["I_c/I_n"] = "R"
["I_c/I_n"] = 10^"R"
"I_c" = "I_n"*10^"R"
The 1906 San Francisco earthquake had a magnitude of 8.3 on the Richter scale
"I_c" = "I_n"*10^8.3
South America there was an earthquake with magnitude 4.9 on the Richter scale
"I_c" = "I_n"*10^4.9
lets compare the intensity of the 1906 San Francisco earthquake with the intensity of the South America earthquake
("I_n"*10^8.3) / ("I_n"*10^4.9) = 10^(8.3 - 4.9) = 10^3.4 = 2511.89
San Francisco earthquake was 2511.89 times more intense than the South American one.