Question

arthquake intensity is given by I = Io(10)m, where Io is the reference intensity and m is magnitude. A particular major earthquake of magnitude 6.0 is 90 times as intense as a particular minor earthquake. The magnitude, to the nearest tenth, of the minor earthquake is

Answer 1

\[\Large I = I_0\cdot10^m\]

if \(I_M\) is the major earthquakes intensity
and \(I_x\) is is the minor earthquakes intensity

\[\Large I_M= I_0\cdot10^6\]\[\Large I_x= I_0\cdot10^x\]

and: \[\Large I_M= 90 \cdot I_x\]

Answer 2

earthquakes =earthquake's

Answer 3

\[\Large \implies{I_M \over I_x}=90\]
\[\Large \implies{\cancel{I_0}\cdot10^6 \over \cancel{I_0}\cdot10^x}=90\]

Answer 4

then take the log of both sides:\[\Large \implies 6-x=\log \left( 90 \right)\]\[\Large \implies \LARGE x=6-\log \left( 90 \right)\]