Logarithms Summary
Academic Skills Advice
What does a log mean?
Log5125 means:
“what power do I need to raise 5 to, to get 125?”
∴ Log5125
=3
(because 53 = 125)
What about ln?
Ln is a special log because it’s base is e (e is a number approximately equal to 2.718)
Example:
Ln 7 means “what power do I need to raise e to, to get 7?”
Ln 7 = 1.946 (3dp) because e1.946 = 7
Remember:
e and ln “undo” each other because they are opposites
Laws of Logs
Log (AB) = Log (A) + Log (B)
e.g. Log (3x2) = Log (3) + Log (2)
𝑨
Log ( ) = Log (𝑨) – Log (𝑩)
𝑩
5
e.g. Log ( ) = Log (5) – Log (4)
4
Log (An) = n log (A)
e.g. log (52) = 2xlog (5)
Log 1 = 0
(using ANY base)
Change of base
1) Given LogxA, find LogyA
LogyA = LogxA x Logyx
Original
Old base
New base
2) If you need a Log in base 10 because that’s all your calculator can do:
LogxA =
© H Jackson 2010 / Academic Skills
Log10A
Log10x
(this works for a change of base to any number not just 10)
1