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how to find log without a logtable

Asked by smarttech2090 24th November 2017, 9:27 PM
Answered by Expert
Answer:
first of all, remember these basic log values,
log 1 = 0
log 2 = 0.3010
log 3 = 0.4721
log 4 = 0.6040
log 5 = 0.6989
log 6 = 0.7781
log 7 = 0.8450
log 8 = 0.9030
log 9 = 0.9542
log 10 = 1
 
These values are applied calculate the log of any number, 
f o m u l a space log space left parenthesis a plus b right parenthesis space equals space log space a space plus space open parentheses fraction numerator b over denominator 2.42 space cross times space a end fraction close parentheses
l e t apostrophe s space t a k e space a n space e x a m p l e space o f space log space 537 space equals space ?
log space 537 space equals log space left parenthesis 5.37 cross times 10 squared right parenthesis
space space space space space space space space space space space space space space space space space space equals space log space left parenthesis 5.37 right parenthesis space plus space log space left parenthesis 10 squared right parenthesis space space space space space space space space space space space space space space space space space space space space space space left square bracket space log space m n space equals space log space m space plus space log space n space right square bracket
space space space space space space space space space space space space space space space space space space space equals space log space left parenthesis 5.37 right parenthesis space plus space 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket space log space 10 to the power of n space equals space n space right square bracket
space space space space space space space space space space space space space space space space space space space equals space log space left parenthesis 5 space plus 0.37 right parenthesis space plus space 2
space n o w comma space a p p l y space t h e space f o r m u l a comma
space space space space space space space space space space space space space space space space space space space equals log space 5 space plus open parentheses fraction numerator 0.37 over denominator 2.42 cross times 5 end fraction close parentheses
space space space space space space space space space space space space space space space space space space space space equals space log space 5 space plus open parentheses fraction numerator 0.37 over denominator 12.1 end fraction close parentheses space
space space space space space space space space space space space space space space space space space space space space space equals space log space 5 space plus left parenthesis 0.0306 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space equals space 0.6989 space plus space 0.0306
space space space space space space space space space space space space space space space space space space space space space space equals space 0.7295
therefore space log space 537 space equals space 0.7295 space plus space 2 space equals space 2.7295
this technic can be applied to any number .
 
Answered by Expert 25th November 2017, 9:46 PM
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