Logarithms

If B^A = C then A is the logarithm of C to base B.

The commonest logarithm base is base 10

eg. 10⁴ =10000

so log₁₀ 10000 = 4

and the antilog₁₀ of 4 is 10000

Many natural processes make use of base 2.718 (base 'e').

This number is common in many natural processes, logs to this base are therefore called natural logarithms.

Log_e is written ln (log natural)

eg. e^2.3= 10

so ln 10 = 2.3

and ln^-1 2.3 is 10

Make sure that you know how to find logs and antilogs to both bases on your calculator.

Multiplication of numbers - add the logs.

log (4 x 2) = log of 4 + log of 2 = 0.602 + 0.301 = 0.903

Division of numbers - subtract the logs

log (4 / 2) = log of 4 - log of 2 = 0.602 - 0.301 = 0.301

The log of a fraction such as a half, is minus the log of the denominator as it is the log of one (zero) minus the log of the denominator

log 0.5 = (log 1 - log 2) = (- log 2) = -0.639