How on earth do I solve? Any help will be much appreciated. The value of M is given by M=a log_(10)S+b. Note: Seismic moment measure the energy of the earthquake.Using the following information, determine the values of a and b and hence find the seismic moment (S) of an earthquake which has a magnetic moment (M) of 7.9. Seismic Moment (S)=4.47xx10^(25), Magnetic Moment (M)=7 Seismic Moment (S)= 2xx10^(27), Magnetic Moment (M)=7.5

Amiya Melendez

Amiya Melendez

Answered question

2022-10-16

Logarithmic problem with 2 variables help
How on earth do I solve? Any help will be much appreciated.
The value of M is given by M = a log 10 S + b
Note: Seismic moment measure the energy of the earthquake.
Using the following information, determine the values of a and b and hence find the seismic moment ( S ) of an earthquake which has a magnetic moment ( M ) of 7.9
Seismic Moment ( S ) = 4.47 × 10 25 , Magnetic Moment ( M ) = 7
Seismic Moment ( S ) = 2 × 10 27 , Magnetic Moment ( M ) = 7.5

Answer & Explanation

bibliothecaqz

bibliothecaqz

Beginner2022-10-17Added 12 answers

You have
M = a log 10 S + b
Then, from the given values you have
(1) 7 = a log 10 ( 4.47 × 10 25 ) + b
and
(2) 7.5 = a log 10 ( 2 × 10 27 ) + b
Subtract ( 1 ) from ( 2 ) yield
7.5 7 = a log 10 ( 2 × 10 27 ) + b ( a log 10 ( 4.47 × 10 25 ) + b ) 0.5 = a log 10 ( 2 × 10 27 ) a log 10 ( 4.47 × 10 25 ) 0.5 = a ( log 10 ( 2 × 10 27 ) log 10 ( 4.47 × 10 25 ) ) 0.5 = a log 10 ( 2 × 10 27 4.47 × 10 25 ) a = 0.5 log 10 ( 2 × 10 27 4.47 × 10 25 )
The value of b can be obtained by substituting a to ( 1 ) or ( 2 )
7 = 0.5 log 10 ( 2 × 10 27 4.47 × 10 25 ) log 10 ( 4.47 × 10 25 ) + b b = 7 0.5 log 10 ( 4.47 × 10 25 ) log 10 ( 2 × 10 27 4.47 × 10 25 )

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