Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

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 .