NATURAL LOGARITHMS

The Constant: e e is a constant very similar to π. Π = … e = … Because it is a fixed number we can find e 2 e e 4

Converting between exponential & natural logs Use our rule from last week to convert y = e x to a logarithm.

Natural Logarithmic We call a log with a base of 10 “Common Log” We can call a log with a base of e “Natural Log” Natural Log is denoted with the “LN” If y = e x then ln y = x

Exponential to Log form 1.e x = 6 2. e x = e x + 5 = 32

Log to Exponential Form 1.Ln 1 = 0 2.Ln 9 = Ln (5.28) =

Solving Exponential Equations 1.e x = 18 2.e x+1 = 30 3.e 2x = 12

Solving Logarithmic Equations 1.Ln x = -2 2.Ln (2m + 3) = Ln x 2 = 6

Natural Log (Ln) & e are inverses