Multiplication of numbers using logarithm

[Shyckh]

I want to multiply two numbers less then 1 and greater then zero but can not be able to understand some step.
Question is y=0.2913x0. 004236
Solution
Logy=log0. 2913+log0.004236
Logy= 1bar.4643+3bar.6269
Logy= 3bar.0912

Bar is for negitive values in log. I want to know how we get 3 bar in last step

 

[blamocur]

This "bar" rotation is rather inconvenient. If you switch to "normal" signed values you get:

log (y) = 0.4643 -1 + 0.6269 - 3 = 1.0912 - 4 = 0.0912 - 3

 

[Dr.Peterson]

I want to multiply two numbers less then 1 and greater then zero but can not be able to understand some step.
Question is y=0.2913x0. 004236
Solution
Logy=log0. 2913+log0.004236
Logy= 1bar.4643+3bar.6269
Logy= 3bar.0912

Bar is for negitive values in log. I want to know how we get 3 bar

What the bar notation means is that only the integer part (characteristic) is taken as negative. So what your work really means is this:

log y = log 0. 2913 + log 0.004236​

log y = (0.4643-1) + (0.6269-3)​

log y = 0.4643+0.6269-1-3 = 1.0912-4= 0.0912-3​

So, assuming the 3 bar you are asking about is the one in the last line, you add the two mantissas, 0.4643+0.6269, and then subtract 4 from the new characteristic, 1, to get -3.