RonrickDaano
Given that 2.004<log10101<2.005, how many digits are there in the decimal representation of 101101?
Clarification: The decimal representation of 210 is 210=1024, which has 4 digits.
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Shadowys
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10101 in binary? then 210 shouldn't be binary....
jishan
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( 101101)base2=( 45)decimal binary no always power of 2 therefore 2power 6= 64
hence 6 digit req..
shubham.bagrecha
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brilliant!
shubham.bagrecha
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it is 101^101
shubham.bagrecha
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@ParthKohli
ParthKohli
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Well, find out \(\log_{10} 101^{101}\)
ParthKohli
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That's it.
shubham.bagrecha
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that is the no. of digits?
ParthKohli
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Yes
shubham.bagrecha
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how log can help calculate no. of digits?
ParthKohli
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Yes, it does. Try it!
shubham.bagrecha
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202 is incorrect
ParthKohli
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You also have to consider the assumptions given in your question.
shubham.bagrecha
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what else is given?
ParthKohli
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Actually, you have to find \(1 + \log_{10} 101^{101}\). Don't write in the answer, let me check first.
ParthKohli
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You can do something else while I check. Thanks :-)
ParthKohli
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203.
ParthKohli
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And so I was correct :-)
shubham.bagrecha
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why add 1?
ParthKohli
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Because the number of digits in \(100\) is not \(\log_{10} 100\), but it's \(1+\log_{10}100\)
shubham.bagrecha
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ok thanks
shubham.bagrecha
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can it be used for counting digits in any expansion?
ParthKohli
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Expansion? You mean number base?
shubham.bagrecha
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like this type of question
ParthKohli
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Yes.
shubham.bagrecha
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ok thanks