find digits if u can

none of these 16 20 18 14

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3 solutions

Noel Lo
Jun 10, 2015

l o g 5 = l o g 10 2 = l o g 10 l o g 2 = 1 0.3010 = 0.6990 log 5 = log \frac{10}{2} = log 10 - log 2 = 1- 0.3010 = 0.6990

l o g 5 20 = 20 l o g 5 = 20 × 0.6990 = 13.98 log 5^{20} = 20 log 5 = 20 \times 0.6990 = 13.98

De Azalea
Jun 8, 2015

5^20 = 25^10, 10^(x-1) = 25^10, x-1 = log (25^10) = 10 x log25 = 13.9, hence x = 14.9, and we run down to 14

Sarvesh Dubey
Jun 7, 2015

Its very easy by logic.... Till 5^4 the number of digits are only 3 but after that the digits add up by 1... So we can predict the number of digits might be 20-4 =16

@Harshi Singh but why did u give the value of log2

sarvesh dubey - 6 years ago

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u hav to solve it by log nt by assumption

Harshi Singh - 6 years ago

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Very right.

Swapnil Das - 5 years, 11 months ago

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@Swapnil Das thank qq genius

Harshi Singh - 5 years, 11 months ago

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@Harshi Singh Hey! I am not a genius. People like Calvin Sir, Daniel Liu and other Mathematics and Physics prodigies in this community can be considered as genius. I am just on a try to become a genius.

Swapnil Das - 5 years, 11 months ago

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