Logarithm In Base 10 Of A Number

Natural Logarithm Of A Number [Base e]

Logarithms

What Is A logarithm?

A logarithm is the power
that you need to raise a base to
in order to generate a number

number = base^{power that you need on the base to get the number}

number = base^logarithm

number = base^power

EXAMPLE
number = base^power
number = (100)
base = (10)
(100) = (10)^power
but
(100) = (10)²
so
the log of 100 in base 10 is 2
log₁₀100 = 2

REMEMBER - Exponent Form
number = base^power

REMEMBER - Logarithmic Form
log_basenumber = power

EXTERNAL LINK What Is A Logarithm?

Exponent Form To Logarithmic Form

Number = Base^Exponent     --->     Log_BaseNumber = Exponent

EXAMPLE
100 is generated by raising the base 10 to the power 2
100 = 10²     --->     Log₁₀100 = 2
The logarithm of 100 in base 10 is 2

EXAMPLE
8 is generated by raising the base 2 to the power 3
8 = 2³     --->     Log₂8 = 3
The logarithm of 8 in base 2 is 3

Logarithmic Form To Exponent Form

Log_BaseNumber = Exponent     --->     Number = Base^Exponent

EXAMPLE
Log₁₀100 = 2     --->     100 = 10²

EXAMPLE
Log₂8 = 3     --->     8 = 2³

Evaluating Logarithms

Product and Quotient Laws of Logarithms

Expanding Logarithms

Condensing Logarithms

Inverse Of A Logarithmic Function

Equivalent Exponential Forms And Solving Exponential Equations

Making Connections Exponential Models

Solving Logarithmic Equations

Graphing A Logarithmic Function

Logarithmic Differentiation

Logarithmic Scales In The Physical Sciences

A Financial Application Of Logarithms

EXTERNAL LINK Advanced Reference - mathworld.wolfram.com