CIE A Level Maths: Pure 3复习笔记2.2.1 Laws of Logarithms

What are the laws of logarithms?

• There are many laws or rules of indices, for example
  • a^m x aⁿ = a^m+n
  • (a^m)ⁿ = a^mn
• 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

How do I use the laws of logarithms?

• Laws of logarithms can be used to …
  • … simplify expressions
  • … solve logarithmic equations
  • … solve exponential equations