Lesson Common and Natural Logarithms

Source code of 'Common and Natural Logarithms'

This Lesson (Common and Natural Logarithms) was created by by Nate(3500)

A logarithm is an easy way to set up an equation in a different way.
To understand, look at a basic idea:
log(b, a) = c
In logarithms, you take the 'b' to the power of 'c' {{{b^c}}} to equal 'a'.
{{{log(8,64) = 2}}}
Looks like: {{{64=8^2}}} and that is right
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Laws of logarithms:
{{{log(a)+log(b)=log(ab)}}}
{{{log(a)-log(b)=log(a/b)}}}
{{{log(a^2)=2log(a)}}}
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{{{Common logs}}} are logarithms with a base of 10 .... they are greatly used in the scientific world today.
Let us try to find the log(1) without a calculator:
log(1)=x
log(10,1) = x
1=10^x
x must be zero
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{{{Natural logs}}} are logarithms with a base of 'e' .... 'e' is the irrational number known as the natural base
Try finding the value for 'x' in e^x=1
e^x=1 original
ln(e^x)=ln(1) take natural log of each side
xln(e)=ln(1) use the law of logarithms
x=ln(1) the natural logarithm of the natural base is equal to one
x=0