Solve each of the following logarithmic equations.
1.The relationship between the surface area A cm^2 and the volume V cm^3
of a sphere can be represented by the following formula:
A=4.836V^n (where n is a constant)
Given that the area of a sphere is 1 000 cm^2 and its volume is2 974cm^3,
find the value of n by using logarithms,and give the answer correct to 3 signficant
figures
ANS:0.667
2.In an experiment to investigate the reproduction of a certain kind of cell,it is
knownthat the number (N) of cells at the t-th hour of the experiment can be
expressed as the following formula:
N=300 log t
If the number of cells at the t-th hour is increased by 90 when compared with
that at 8 hours ago,find the value of tcorrect to the nearest integer.
ANS:9.0*10^9
3.Accordind to a research of oceanography, for every metre that a diver goes
down,the light intensity will increase by 2.5%.How many metres should a diver
go such that
(a)the light intensity is one fourth of that at the water surface?
(b)the light intensity is 1%of that at the water surface?
(give the anwers correct to the nearest integer)
ANS:(a)55m
(b)182m
F.4 MATHS
2010-03-06 9:28 pm
回答 (1)
2010-03-09 3:25 am
✔ 最佳答案
1. A=4.836V^n1000=4.836*2974^n
LOG(1000/4.836)=n LOG 2974
n=0.667
2. N=300 LOG t
90=300 LOG t - 300 LOG(t-8)
90/300= LOG t - LOG (t-8)
0.3= LOG [ t / (t-8) ]
10^0.3= t / (t-8)
t=10^0.3(t-8)
t=10^0.3t-10^0.3(8)
10^0.3(8)=10^0.3 t - t
10^0.3(8)=t(10^0.3-1)
t=[10^0.3(8)] / (10^0.3-1)
t=16
PS: ans應該係16,你可能睇錯答案,因為我本書同你一樣
3. (a) (1-2.5%)^n=1/4
97.5%^n=1/4
0.975^n=1/4
n LOG 0.975=LOG(1/4)
n=55(give the anwers correct to the nearest integer)
(b) (1-2.5%)^n=1%
97.5%^n=0.01
0.975^n=0.01
n LOG 0.975=LOG 0.01
n=182(give the anwers correct to the nearest integer)
收錄日期: 2021-04-23 18:25:51
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