Math CentralQuandaries & Queries


Question from Yahweh, a student:

Lets say I have two very large numbers in the form of a^b:
727464^512693 and 624610^518548

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.

Stephen La Rocque


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