# Logarithms

Whenever you see the words log or logarithms write down the following:

`Log_2(8)=3`

And write down

What is the power on 2 that gives 8

## Logs explained

`Log_2(8)=3`

This says:

What is the power on 2 that gives 8

`2^? = 8`

The only answer is 3

i.e. `2^3 = 8`

## For any log

From the above `Log_ab`

Logarithm is the power on “`a`” that gives the result “`b`”

**Examples**

1. What is `Log_3 81`

Write out what you know

We know `Log_2 (8) = 3`

and this means “what is the power of `2` that gives `8`”

and that equals `3`

Therefore `Log_3 81`

This says what is the power on `3` that gives `81`

`3^?` | `= 81` |

`3times3` | `= 9` |

`3times3times 3` | `= 27` |

`3\times 3\times 3\times 3` | `= 81 (4\ t\im\es)` |

Therefore Answer: `4` is the power on `3` that gives `81`

That is `3^4 = 81`