Lesson An overview to the laws of logarithms

Source code of 'An overview to the laws of logarithms'

This Lesson (An overview to the laws of logarithms) was created by by HyperBrain(694)

: View Source, Show
About HyperBrain: As I help you solve the problem, you are helping me practice my skills.

very first---the logarithm of a number n is the the exponent of 10 where 10 should be raised to obtain b. EXAMPLE---{{{log(100)=2}}} because {{{10^2=100}}}

First I will tackle the most basic laws: the logarithm of a product and the logarithm of a quotient.

logarithm of a product:

{{{log (xy)=log (x) + log(y)}}}

logarithm of a quotient:

{{{log(x/y)=log(x)-log(y)}}}

This are the Foundations of the this law: logarithm of powers

{{{x^n}}} is defined as x multiplied n times to itself.

Thus,
{{{log(x^n)=n log(x)}}}

This is similar to the logarithm of roots.

Remember that roots can be expressed as fractional exponents.
So, square root of x={{{x^(1/2)}}}, cube root of x={{{x^(1/3)}}} and so on.

Thus,

log(x^(1/n))=(1/n) log (x).

Now let's recall this identity: log(1)=0

So, let us formulate the logarithm of reciprocals.

{{{log(1/x)=0-log (x)}}}
________={{{- log(x)}}}

And, in modern math, negative logarithms are called COLOGARITHMS!

Please watch our music video at http://www.metacafe.com/watch/1101445/science_avenue/ rate and leave a comment