How to prove that log is an injective function?
Log is an Injective function?
2009-10-01 5:17 am
回答 (1)
2009-10-01 6:07 am
✔ 最佳答案
(1) Algebraic method:log x1 = log x2
log x1 - log x2 = 0
log (x1/x2) = 0
x1/x2 = 1
x1 = x2
(2) Calculus method:
d(log x)/dx = d[(ln x)/(ln 10)]/dx
= 1/(x ln 10)
So in the domain of log, i.e. all positive real values of x, d(log x)/dx > 0 and hence log x is strictly increasing.
In conclusion, log x is injective.
參考: Myself
收錄日期: 2021-04-23 22:16:26
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