I need to propagate a few uncertainties for logarithmic numbers, using the following two formulas:

For: $\displaystyle base 10 x = log_{10} a$

$\displaystyle s_x=0.434(\frac{s_a}{a})$

where:

$\displaystyle s_x=$ uncertainty in result

$\displaystyle s_a=$ uncertainty in numbers used for calculation

$\displaystyle a=$ numbers used for calculation

AND

For: $\displaystyle base 10 x = 10^a a$

$\displaystyle s_x=2.303\cdot x\cdot s_a$

where:

$\displaystyle s_x=$ uncertainty in result

$\displaystyle x=$ result of calculation

$\displaystyle s_a=$ uncertainty in numbers used for calculation

My question is, what exactly are the 0.434 and 2.303 values for? I assume they're to counter something that log calculations add?