Embedded Files
Mantra: A Logarithm is an Exponent
Log – General
Log – General
Common Log
Common Log
Natural Log
Natural Log
“Log base b of y is x”
If the base is not given, assume 10
Natural Log: “l” “n” of “y” is “x”
A logarithm is the exponent or power to which a base must be raised to yield a given number:
A logarithm is the exponent or power to which a base must be raised to yield a given number:
Euler designed e and ln to have magical properties special made for calculus.
Euler designed e and ln to have magical properties special made for calculus.
Logs to the base "e" (2.71828...), a transcendental number, are called natural logs and are written as ln.
Rules of Logarithms:
Rules of Logarithms:
Since logarithms are nothing more than exponents, these rules come from the rules of exponents:
Where a, b, x and y are real numbers not equal to zero.
Some convenient properties of our friends
Some convenient properties of our friends
Change-O-Base
Change-O-Base
Since e and ln were created to have special calculus properties we often want to change base to e.
Change Base General (base b to base a)
Change Base General (base b to base a)
Example 1
Example 2
Page updated
Google Sites
Report abuse