Power Log Zero Returns as Zero?

Question

wesleynotwise 2017-6-11

0
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https://ww2.mathworks.cn/matlabcentral/answers/344269-power-log-zero-returns-as-zero

评论： wesleynotwise 2017-6-11

Can someone solve this maths mystery in Matlab? why log(0) returns as -Inf, but 5^log(0) returns as zero?

log(0)
ans =
-Inf
5^log(0)
ans =
0

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Answer 1

John D'Errico 2017-6-11

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https://ww2.mathworks.cn/matlabcentral/answers/344269-power-log-zero-returns-as-zero#answer_270361

编辑：John D'Errico 2017-6-11

在 MATLAB Online 中打开

Um, basic math?

1. The log function is singular at zero. Log(x) approaches -inf, as x approaches zero. So this seems clear.

2. What is 5 raised to some large positive power? A big number.

3. What is 5 raised to some large negative number? It is the inverse of the answer to #2. So a TINY number.

4. What is the smallest number you can represent in double precision without an underflow to zero?

5^-462
ans =
9.8813e-324
5^-463
ans =
     0
realmin
ans =
  2.2251e-308

Realmin for a double is 2.2251e-308, but since you can have what are called denormalized numbers, you can go just a bit further before doubles just give up.

5. Is infinity larger than 463? Last time I checked, yes, it was.

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Stephen23 2017-6-11

"I always thought that anything associated with an infinity will result in infinity"

What about 1/N as N->inf? You really should complain to your high school that they did a bad job.

wesleynotwise 2017-6-11

Nah, I blame myself for not paying attention in the class. Bad student. if 1/N and N -> Inf, I would say it is close to zero, But if 1/ Inf, I would say it is infinity.

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