**Key Facts:**

The functions

y = a^{x} or f(x) = a^{x}

where a is a constant, are exponential functions

a^{x} = n means that log_{a}n = x

where a is called the base of the logarithm

log_{a}1 = 0

Any number to the power 0 is 1, x^{0} = 1 or a^{0} = 1

log_{a}a = 1

Any number to the power 1 is just the number itself, 10^{1} = 10,

6^{1} = 6 or a^{1} = a

Multiplication law

log_{a} xy = lag_{a} x + log_{a} y

Division law

log_{a} (x/y) = log_{a} x – log_{a} y

Power law

log_{a} (x)^{k} = k log_{a} x

From the power law

log_{a} (1/x) = -log_{a }x

Equations of the form a^{x} = b can be solved by taking logarithms (to base 10) of each side

Change of base rule

log_{a}x = (log_{b}x)/(log_{b}a)

From the change of base rule

log_{a}b = 1/log_{b}a

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.

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