Some useful calculations to keep in mind !!

> changing bases in logarithms: log_{a} x = log_{b} x / log_{b} a

for base 10 and *e*: log x = ln x / ln 10

(log *e* = 1 / ln 10)

> derivative of exponential with other base:

d (a^{x}) / dx = a^{x} ln a

in the case of base 10: d (10^{x}) / dx = 10^{x} ln 10

> derivative of logarithm with other base:

d (log_{a} x) / dx = d (ln x / ln a) / dx = 1 / ( x ln a)

so in the case of base 10: d (log x) / dx = 1 / ( x ln 10)

A useful online resource for calculations is Wolfram Alpha ‘s engine.