Functions - Logarithms - Log Laws.
Summary of the Laws and ways to impement.
The six main laws for manipulating logarithms as presented in the video are summarised below:
1. | loga a = 1 | Use immediately. |
2. | loga 1 = 0 | Use immediately. |
3. | loga (xy) = loga x + loga y | Use after ensuring that there are no values in front of the log terms (if so, use Law 5) and that the logs being combined have the same base. |
4. | Same as above. | |
5. | loga xn = n loga x | Be careful the index applies to only one term after the log.
Sometimes the terms should be split up (using Law 3 or 4) - eg for logaxy2 = logax + 2logay. The index CANNOT apply to the whole expression (viz: (loga xy)2 cannot be simplified). |
6. | Especially useful when manipulating terms for calculus. |
We could also add another simplification to this list but it is not a law.
The expression in red should be recognised - if a number is raised to the power of a logarithm with the same base as the number, the value of the expression is simply the number after the log term.
So .