HomeThe question looks like this:
10001001 (?) 10011000We want to find the (?) operator.
I scribbled that a moment ago. I'm using logarithm, and captured the typed-steps as an image.
Let's start
Hang on for a moment...
In conclusion
Without using calculator,
10001001 is larger than 10011000
10001001 > 10011000
Closure
As I observed, that pattern starts from integer greater than 2 (to any large positive integer).
I haven't tinkered the positive "infinity". I suppose it will be the same.
It's like imagination, the infinity concept.
And for number with, like, floating point, you can do your own scribbling.
Anyway, if we use 1 (in that pattern above):
12 (?) 21
1 (?) 2
1 < 2
If we use 2:
23 (?) 32
8 (?) 9
8 < 9
The next one, 3:
34 (?) 43
81 (?) 64
81 > 64
Next, 4:
45 (?) 54
1024 (?) 625
1024 > 625
And so on...
This technique will surely result different outcome for integer less than or equal to 2. Especially on the Let's assume it's 1 step (rounding down step).
Wolfram and Wikipedia
This is the link on Wolfram|Alpha about that particular question.
This is the the form equivalency and decimal approximation of log1000(1001) on Wolfram|Alpha.
This is the list of logarithmic identities on Wikipedia.
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