Lesson An overview to the laws of logarithms
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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