急問, 點解log個底唔可以係負數呢

log_a x = y
姐係解 a^y = x
要解y的話.. y log a = log x
y = log x / log a
如果 a 係負數.. log_10 a = b
10^b = a
咁10^b 係出唔到負數, 只可以apporaches to 0.
所以a 唔可以係負數
同理 a^x = a^y , x 要等於y 姐係 log a 要存在..所以a要係大過0
而且 log 1 = 0 計算時會出現 log a 在分母..會出現undefined..
所以a 唔等於1

I like the another one more.

a^x = a^y
a^(x - y) = 0
if a> 0, a^z = 0 if and only if z = 0, i.e. x = y
if a = 1, a^z = 0 for any z, not necessary 0,
so y - x is not necessary 0, i.e. x is not necessary equal to y

if a < 0, a^z is not a real number if z is not an intger
e.g. if a = -1, z = 0.5, a^z is the squart root of -1, which is an imaginary number

so the base of the logarithm cannot be less than 0 if you are talking about real numbers only

in other words, the base of the logarithm can be negative if you also consider imaginary numbers.

2007-06-20 10:14:14 補充：
根本冇解釋到問題o既本質, 調o黎調去然後話undefined
a 係負數o既話, 你log a o個個step已經冇o左啦
如果問你點解唔可以計log 負數? 你話調返轉頭話log 個底唔可以負數呀?