F.4 maths 10分

3(a)
Let the sound intensity in the classroon amd on the street be I_1 and I_2 resp.
Then from the given,
10log I_1 = 65
10log I_2 = 90
10log I_2 - 10log I_1 = 25
log(I_2/I_1) = 2.5
I_2/I_1 = 10^2.5
= 316

Thus the intensity on the street is 316 times as large as that in the classroom.

(b)Let I_3 be the sound intensity of the sound from the building. Then
I_3 = 70 x I_2
10log I_3 - 10log I_2 = 10log(70 x I_2) - 10log I_2
= 10log 70 + 10log I_2 - 10log I_2
= 10log 70
= 18.4

So, the intensity from the building site is 18.4 dB greater than that from the street and its value of sound intensity is 90 + 18.4 = 108.4 dB
1 if log4=a and log3=b then log18=?
log18
=log(2*3*3)
=log2+2log3
=a+3b
2 if 2=10^P ,express log(1/5) in terms of p
log(1/5)
=log(2/10)
=log2-log10
=10^p-1

for the intensity level, myisland has done correctly, but something wrong for the following part....

1.if log4=a and log3=b then log18=?
log18=log (2 x 3 x 3) = log 2 + 2 log 3 = 1/2 * log 4 + 2 log 3 = a/2 +2b

2.if 2=10^P ,express log(1/5) in terms of p
log(1/5) = log(2/10) = log 2 - log 10 = log 10^p - log 10 = p - 1