Logarithm Basics

The logarithm base a of b is the exponent you put on a to get b:

i.e. Logs give you exponents!

Definition of Logarithm

if and only lo

ifga

x

b x

a b

a > 0

and

b > 0

Logarithm and Exponential Forms

5 = log2(32)

25 = 32

Logarithm Form

Exponential Form

Base Stays the

BaseLogs Give you

Exponents

Input Becomes

Output

ExamplesWrite each equation in exponential form

1.log125(25) = 2/3

2.Log8(x) = 1/3

Write each equation in logarithmic form

1.If 64 = 43

2.If 1/27 = 3x

1252/3 = 25

81/3 = x

log4(64) = 3

Log3(1/27) = x

Original Inverse

Inverse of an Exponential Equation

Log’s give you exponents!

2xy 2yx

2logy xOR