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prove that

Logea=2.303log10a

Asked by nitishkrnehu09 9th October 2017, 11:11 PM
Answered by Expert
Answer:
begin mathsize 16px style log subscript straight e space straight a space equals space fraction numerator log subscript 10 space straight a over denominator log subscript 10 space straight e end fraction space space space space space space space space space open parentheses using space base space change space formula space in space logarithm close parentheses
log subscript straight e space straight a space equals fraction numerator log subscript 10 space straight a over denominator log subscript 10 space end subscript 2.718 end fraction space open parentheses space straight e space equals space 2.718 close parentheses
Taking space log space for space log subscript 10 space end subscript 2.718 comma
log subscript straight e space straight a space equals fraction numerator log subscript 10 space straight a over denominator 0.4343 end fraction
log subscript straight e space straight a space equals 2.303 space log subscript 10 space straight a space space space space space space space space space open parentheses fraction numerator 1 over denominator 0.4343 end fraction space equals space 2.303 close parentheses
end style
Answered by Expert 18th December 2017, 10:55 AM
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