prove that

Logea=2.303log10a

Asked by nitishkrnehu09 | 9th Oct, 2017, 11:11: PM

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 Sneha shidid | 18th Dec, 2017, 10:55: AM

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