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
- 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.