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`
