Laws of Logarithms (Cambridge (CIE) A Level Maths) : Revision Note
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Laws of Logarithms
What are the laws of logarithms?

There are many laws or rules of indices, for example
am x an = am+n
(am)n = amn
There are equivalent laws of logarithms (for a > 0)

There are also some particular results these lead to

Two of these were seen in the notes Logarithmic Functions
Beware …
… log (x + y) ≠ log x + log y
Results apply to ln too
In particular
and
How do I use the laws of logarithms?
Laws of logarithms can be used to …
… simplify expressions
… solve logarithmic equations
… solve exponential equations
Examiner Tips and Tricks
Remember to check whether your solutions are valid. log (x+k) is only defined if x > -k.
You will lose marks if you forget to reject invalid solutions.
Worked Example

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