logarithms

Question

2 pow 64 not 264

Answer 1

$20$ should be the correct answer.

To find the number of digits(not bits) in a number, say $x$, we need to find the ceiling of log base ten of $x$, that is $\left \lceil \log_{10}x \right \rceil$.

Given $\log{2} = 0.30103$, it seems a bit incomplete as the base of logarithm is not mentioned.

However since $10^{0.30103} \approx 2$, so it can be inferred that in $\log{2} = 0.30103$ the base of log should be $10$.

Coming to the original question, the number of digits in $2^{64}$ would be $\left \lceil \log_{10}\left ( 2^{64} \right ) \right \rceil = \left \lceil 64\log_{10}2 \right \rceil = \left \lceil 64 \times 0.30103 \right \rceil = \left \lceil 19.26592 \right \rceil = 20.$

Comments

i want 2 pow 64..you found log(2 pow 64)

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As you mentioned in the question, I calculated the number of digits in $2^{64}$ and not in $\log\left ( 2^{26} \right )$.

We need to calculate the ceiling of log base 10 of the number we are interested in, so following the process, I came across $\log\left ( 2^{26} \right )$.

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iam nt understanding..iam sorry

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tell this also

A boy travelling from his home to school at 25 km/hr and came back at 4 km/hr. If whole journey took 5 hours 48 min. Find the distance of home and school.