NUMBAT OER - Open Educational Resources

3. Introducing the notation used for variables

This section introduces the ways of representing a variable and the simple transformations (powers, roots and logarithms) that may be applied to it. In the following table, the variable is given the symbol 'a'.

a A variable
a2 The variable a squared (raised to the power 2)
ax The variable a raised to the power x (where x need not be a whole number)
a-1 The reciprocal of a (that is one divided by a)
a-2 The reciprocal of a-squared (that is one divided by a2)
a-x The reciprocal of a raised to the power x
a1/2 or a0.5 The square root of a
a1/x The 'xth' root of a
log(a) or log10(a) The logarithm to the base 10 of a
ln(a) The logarithm to the base e of a (also called the 'natural' logarithm of a)
exp(a) or ea The quantity e raised to the power a (also called the exponent of a)

Logarithms and exponents are explained in this resource