Expert: Sherman D. - 11/17/2007

Question
How do one go about making sense out of the logarithmic tables? Namely the characteristics and the mantissas. For instance in the table it indicates that the log of 3.6 is 0.55630 and the log of 36 is 1.55360 etc.etc.My question is,how does one get 3.6 out of 0.55630 and 36 out of 1.55630?

Answer
using the laws of logarithms and exponents

log(3.6) = .55630

using inverse of operations, you get

10^(.55630) = 3.6

Here's something more complex to understand
log(3.6) = log(36/10) = log(18/5) = log(18) - log(5), now if you were to take that further, log(18) - log(5) = log(9 * 2) - log(5) = log(9) + log(2) - log(5) = log(3^2) + log(2) - log(5) = 2log(3) + log(2) - log(5)

as for going from log(3.6) = .5563 to log(36) = 1.5563

thats easy to explain

log(36) is nothing more than saying log(3.6 * 10), now jusing laws of logarithms, log(3.6 * 10) = log(3.6) + log(10)

we already know what log(3.6) was from the previous work, and log(10) = 1

so now you have

log(36) = log(3.6 * 10) = log(3.6) + log(10) = .5563 + 1 = 1.5563

and there you have it.