Logarithm
Created | Updated Feb 3, 2004
In it's most basic explanation, a Logarithm reverses an exponent.
For the first pass at this article I am simply going to use Log to mean the Natural Logarithm (the Logarithm with base e).
I intend to someday add a proper discussion of base 10 and base e logs.
The natural log is basically a function to remove the number e from an equation. So:
log(e^x)=x
e^(log(x))=x
It can be used to solve equations with exponents in them. Such equations occur with unnatural frequency when solving upper level mathematics problems.
The most basic use of Log to solve for y:
e^y=x
log(e^y)=log(x) <--- Take a logarithm against both sides
y=log(x) <--- log(e^y) is just y
Helpful Rules regarding logs:
log(xy) = log(x) + log(y)
log(x/y) = log(x) - log(y)
log(c*x) = c * log(x)
Applications
<li>Decibel measurements of sound
<li>Designing Sliderules
<li>Solving differential equations
<li>Solving calculus equations
For the first pass at this article I am simply going to use Log to mean the Natural Logarithm (the Logarithm with base e).
I intend to someday add a proper discussion of base 10 and base e logs.
The natural log is basically a function to remove the number e from an equation. So:
log(e^x)=x
e^(log(x))=x
It can be used to solve equations with exponents in them. Such equations occur with unnatural frequency when solving upper level mathematics problems.
The most basic use of Log to solve for y:
e^y=x
log(e^y)=log(x) <--- Take a logarithm against both sides
y=log(x) <--- log(e^y) is just y
Helpful Rules regarding logs:
log(xy) = log(x) + log(y)
log(x/y) = log(x) - log(y)
log(c*x) = c * log(x)
Applications
<li>Decibel measurements of sound
<li>Designing Sliderules
<li>Solving differential equations
<li>Solving calculus equations
