## 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 |

a^{2} |
The variable a squared (raised to the power 2) |

a^{x} |
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 a^{2}) |

a^{-x} |
The reciprocal of a raised to the power x |

a^{1/2} or a^{0.5} |
The square root of a |

a^{1/x} |
The 'x^{th}' root of a |

log(a) or log_{10}(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 e^{a} |
The quantity e raised to the power a (also called the exponent of a) |

Logarithms and exponents are explained in this resource