Additional, mathematically equivalent forms of the Colebrook equation are:
::where:
:::1.7384... = 2 log (2 &times; 3.7) = 2 log (7.4)
:::18.574 = 2.51 &times; 3.7 &times; 2
and
:or
::where:
:::1.1364... = 1.7384... &minus; 2 log (2) = 2 log (7.4) &minus; 2 log (2) = 2 log (3.7)
:::9.287 = 18.574 / 2 = 2.51 &times; 3.7.
The additional equivalent forms above assume that the constants 3.7 and 2.51 in the formula at the top of this section are exact.  The constants are probably values which were rounded by Colebrook during his curve fitting; but they are effectively treated as exact when comparing (to several decimal places) results from explicit formulae (such as those found elsewhere in this article) to the friction factor computed via Colebrook's implicit equation.
Equations similar to the additional forms above (with the constants rounded to fewer decimal places, or perhaps shifted slightly to minimize overall rounding errors) may be found in various references.  It may be helpful to note that they are essentially the same equation.