Logarithms

What is to be learned? How to translate a log statement

Previously Exponentials are in form y = ax Logs are their inverse

(2 , ) 16 y = 4x y = x y = log4x 1 (16 , 2) 1

y = log4x y = logax 2 = log416 x = ay 42 = 16 y = log4x (16 , 2) (x , y) 1

x a statement logax = y translation x = a (starting no.) (power) (power) a (base) (base) (base)

Using Logs log2 x = 4 4 x = 2 x = 16 log5 x = 3 3 x = 5 x = 125

Using Logs log10 1000 = t t 1000 = 10 t = 3 logr 8 = 3 3 r 8 = r = 2

Using Calculator log10 1000 = x 1000 = 10 x = 3 log log = ln (natural log) e

Logarithms starting no. statement logax = y power base translation x =

Using Logs log7 x = 3 3 x = 7 x = 343 log5 625 = h h 625 = 5 x = 4

logr 1000000 = 6 6 r 1000000 = r = 10

On Calculator log is log 10 log is ln (natural log) e