MHB How Many Digits Does 2^1000 Have?

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The number of digits in \(2^{1000}\) can be calculated using the formula for the number of digits in a number, which is given by \( \lfloor \log_{10}(n) \rfloor + 1 \). With \( \log_{10}(2) \approx 0.301\), the calculation shows that \(2^{1000}\) contains 302 digits. Participants in the discussion confirmed this result and expressed satisfaction with the solution. The mathematical approach was appreciated for its clarity and efficiency. Overall, the challenge was successfully resolved with a straightforward calculation.
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Thought this challenge was worth asking here :D

Using mathematics, how many digits does the number $$2^{1000} $$contain?
 
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Farmtalk said:
Thought this challenge was worth asking here :D

Using mathematics, how many digits does the number $$2^{1000} $$contain?

Because is $\log 2 \sim .301$, then $2^{1000}$ has 302 digits... Kind regards$\chi$ $\sigma$
 
Nice! I thought it would take a little longer to figure that out! Correct answer!:D
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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