How many digits does 225964951−1 have?

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retopire07c · Accepted Answer

Step 1Taking the 10-logarithm is basically the easiest way to do it. Remember to always round down, no matter what the decimal part is (for instance, log10(99)+1≈2.996, and we want the answer to be 2).However, if all you have is a classic calculator that won&#039;t work with such large numbers, or you want to get an approximate answer with just mental calculations, some more manipulations must be done first.Start with noting that 225,964,951−1 and 225,964,951 have the same number of digits. From there, we know thatlog10(225,964,951)={25,964,951}⋅log10(2)And then either let the calculator do the work, or if you go the mental route, know that log10(2)≈0.3 (from 210≈103) and just get{25,964,951}⋅log10(2)≈7,800,000For the mental calculation, adding 1 here (although it&#039;s technically what you&#039;re supposed to do) makes no sense in my opinion.

How many digits does 2^{25964951}-1 have?

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