指數及對數函數

a.
函數y=3^(x-1)的略圖
利用該圖像，解不等式：3^x<18

The graph shows that the function is monotonically increasing from -inf, and reaches y=18 at about 3.6.
See:
http://i263.photobucket.com/albums/ii157/mathmate/math/3_x-1.png

Therefore,
f(x)=3^x<18
is for all (x-1)<3.6, or x<4.6.
More precisely, x<4.6309... = 1+1+log(18)/log(3)

b.
計算在下列各不同震級的地震中所釋放出的能量。(答案準確至三位有效數字。)
(i) 黎克特制2級
(ii) 黎克特制3級
(i) Intensity 2 on the Richter scale is equaivalent to the detonation of one metric tonne of TNT explosive, and the energy is released is 1 GJ (giga joules, or 10^9 joules).
(ii) When the intensity is increased by 2, the energy is increased by 1000 times, which means that for every unit increase in intensity, the energy is increased by 10^(3/2) times, or 31.622 times.
Thus for an intensity of 3, the energy released is 1GJ*31.622=31.622 GJ.


2007-12-17 11:27:30 補充：
函數y=3^(x-1)的略圖<a title="figure"><img src="http://i263.photobucket.com/albums/ii157/mathmate/math/3_x-1.png">函數y=3^(x-1)的略圖 </a>