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 ):

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