1. (a) log 12 + log (8 1/3)
(b) log 0.07 - log 70
2 .(a) 1/2 log 5^2 + 1/3 log 2^3
(b) log 81 / log 9
3. (a) log x^4 / log x
(b) log x + log 2 - log 2x
(c) log x + log 1/x
4. (a) 10^(3x) = 1000
(b) 20^x = 40
(c) 10^x = 0.7
(d) 40^(x/6) = 500
5. Alex deposits a sum of money in a bank. it is known that the
amount $A that he can receive after n years is given by the
following formula :
A = 2000 x 1.07 ^n
At least how many years later can Alex receive an amount
more than $2800?
6. Transform each of the following given equations into a linear
equation, then sketch the graph and state wheather the
graph passes through the origin.
7. The energy released during an earthquake is 3 x 10^21
units. Using the formula relating the energy and magnitude
of the earthquake, find the magnitude of this earthquake.
8. The intensity level of the sound produced during a concert is
92 dB. What is the intensity (in W/m^2) of the sound
F.4 math (indices and logarit)
2011-08-28 11:02 am
回答 (1)
2011-08-28 6:57 pm
✔ 最佳答案
1. (a) log 12 + log (8 1/3)=log(12x81/3)=log324 (b) log 0.07 - log 70=log(0.07/70)= log(1/1000)=log10^(-3)= -32 .(a) 1/2 log 5^2 + 1/3 log 2^3= log 5^(2/2) + log2(3/3)= log5 + log2= log10= 1(b) log 81 / log 9= log9^2/log9=2log9/log9= 23. (a) log x^4 / log x= 4logx/logx= 4(b) log x + log 2 - log 2x=log(2x/2x)= log1= 0(c) log x + log 1/x= log(x/x)=log1=04. (a) 10^(3x) = 1000 10^(3x) = 10^3∴ 3x = 3x = 1
(b) 20^x = 40
log 20^x = log 40xlog 20 = log 40x = log40/log20 = 1.231378 = 1.23 corr.to 3 sig.fig.
(c) 10^x = 0.7log 10^x = log 0.7xlog 10 =log 0.7x = log0.7 = -0.1549 = -0.155 corr.to 3 sig.fig.
(d) 40^(x/6) = 500 log 40^(x/6) = log 500(x/6) log 40= log 500x/6 = log500/log40 x/6 = 1.684687.... x = 10.108123... = 10.1 corr.to 3 sig.fig.5........2000(1.07)^n > 2800log 2000(1.07)^n > log 2800 log 2000 + log(1.07)^n > log 2800 log(1.07)^n > log 2800 - log2000nlog1.07 > log1.4n > log1.4/log1.07n > 4.9735 years later ................... 6????? 7 find the magnitude of this earthquake.log(E) = 11.4 +1.5(R)log3x 10^21 = 11.4 +1.5(R)
1.5(R) = log3x 10^21 - 11.4
1.5(R) = 10.07712125R =6.718 the magnitude of this earthquake= 6.72 corr.to 3 sig.fig. 8. The intensity level of the sound produced during a concert is
92 dB. What is the intensity (in W/m^2) of the sound (D) dB = 10log(I/10^-12)92 = 10log(I/10^-12)9.2 = log(I/10^-12)9.2 = log(I) - log10^-129.2 + (-12) = log(I)log(I) = -2.8I = 10^-2.8= 0.0015849 the intensity (in W/m^2) of the sound = 0.00158 (W/m^2) corr.to 3 sig.fig.
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