Key Facts:

The functions

y = ax or f(x) = ax

where a is a constant, are exponential functions

ax = n means that logan = x

where a is called the base of the logarithm

loga1 = 0

Any number to the power 0 is 1, x0 = 1 or a0 = 1

logaa = 1

Any number to the power 1 is just the number itself, 101 = 10,

61 = 6 or a1 = a

Multiplication law

loga xy = laga x + loga y

Division law

loga (x/y) = loga x – loga y

Power law

loga (x)k = k loga x

From the power law

loga (1/x) = -loga x

Equations of the form ax = b can be solved by taking logarithms (to base 10) of each side

Change of base rule

logax = (logbx)/(logba)

From the change of base rule

logab = 1/logba

For the OCR, you need to remember all of the above key points. For Edexcel, only the change of base rule is given in the formulae booklet, everything else you need to remember.