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help asked in 科學及數學數學 · 8 years ago

急 ! Logarithmic Function EX3.

請詳細步驟教我計下條 :

(不要網址回答)

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  • 8 years ago
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    (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
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