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| Math Central | Quandaries & Queries |
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Question from Yahweh, a student: Lets say I have two very large numbers in the form of a^b: I want to calculate which number is larger, but its unreasonable to type these numbers into a spreadsheet to get an answer right away. How could I determine the larger or the two numbers efficiently? |
Hi Yahweh.
Try using logarithms.
If log a > log b then a > b.
One of the niceties of logarithms is that exponents become factors: that's much easier to deal with.
Using common (base 10) logarithms,
log (727464512693) = 512693 x log (727464) = 512693 x 5.861811506 = 3005309.7
log (624610518548) = 518548 x log (624610) = 518548 x 5.795608933 = 3005301.4
Thus the first of the two is larger.
Cheers,
Stephen La Rocque
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