What is the logarithm of .0856?

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Answer 1 · 2016-04-12T11:49:34

#3log2+log107-4~=-1.067526=-2+0.932474#

#0.0856=856/(10,000)=(2^3*107)/10^4#

So

#log 0.0856=log(2^3*107)/10^4=log2^3+log107-log10^4#
#=3log2+log107-4~= -1.067526# [1]

Using a Logarithm Table:
(for instance, in http://myhandbook.info/table_commonlog.html)

#=3*(0.301030)+(2+0.029384)-4#
#=-2 +0.903090+0.029384#
#=-2+0.932474#

More direclty, one could also use

#=-2+log8.56#
#=-2+0.932474#

Converting the result [1] (obtained using a calculator) to the format #"Characterisc#+#Mantissa#
(see http://www.math-for-all-grades.com/CharacteristicandMantissa.html ):

#-1.067526=(-1-1)+(1-0.067526)=-2+0.932474#