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help asked in 科學及數學數學 · 8 years ago

# 急 ! Logarithmic Function EX3.

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• 8 years ago

(a)let E1 and E2 be the amplitude of the seismic wave in the first and secong earthquake respectively.

logE1=1.5(8.1)+K.....(1)

logE2=1.5(7.5)+K......(2)

(1)-(2)

logE1-logE2=(1.5(8.1)+K)-(1.5(7.5)+K)

log(E1/E2)=1.5(8.1)-1.5(7.5)

=0.9

E1/E2=10^0.9

=8(corr.to the nearest integer)

the amplitude of the scismic wave in the first earthquake was 8 times as the second one.

(b)let E1 and E3 be the amplitude of the seismic wave in the first and third earthquake respectively,

logE1=1.5(8.1)+K......(1)

logE3=1.5(7.0)+K......(2)

(1)-(2)

logE1-logE3=(1.5(8.1)+K)-(1.5(7.0)+K)

log(E1/E3)=1.5(8.1)-1.5(7.0)

=1.65

E1/E3=10^1.65

=45(corr.to the nearest integer)

the amplitude of the scismic wave in the first earthquake was 45 times as the third one.

(b)let I W/m^2 be the sound intensity of a flying civil aircraft.

122=10log(10^12I)

12.2=log(10^12I)

10^12I=10^12.2

I=10^12.2/10^12

I=10^0.2

I=1.58(corr.to 3 sig.fig.)

intensity level of the moving car

=10log(10^12*10^0.2/10000)

=82dB.

Source(s): me