Logarithmic+Graphs

**__Logarithmic Graphs__**

 * Geometer's sketchpad document:

> > logk ab= logk a + logk b > > Let logk a=x, then a=k^x > logk b=y, then b=k^y > logk ab=z, then ab=k^z > > Now substitute a and b: > ab=k^z > K^x*K^y=k^(x+y) > K^x*K^y=k^z > > __**NOTE:**__ K must be greater than zero.The base can't be a negative value and k cannot equal 1. Why?
 * Definition of logarithmic functions : Logarithmic functions are the inverse of exponential functions. Here's an example that will clarify that stating:

e= 2.718281...
 * Definition of natural logarithms: logarithms that have the base 'e'. Natural logarithm of the number 'x' is the power to which 'e' would have to be raised to be equal to 'x'. x=e^y


 * __NOTE:__** lnx=loge x


 * **__Logarithmic laws__**

__Power law:__ loga b^x = xloga b e.g. log2 16^3=3log2 16

__Product law:__ loga b+loga c= loga bc e.g. log5 (25*625)=log5 (25) + log5 (625) log5 (5)^6= log5 (5)^2 + log5 (5)^4

__Quotient law:__ loga b-loga c= loga (b/c) e.g. log2 (4/3)= log2 4-log2 3

__Special logarithms:__ loga a=1 loga 1=0

__Base changing:__ logk x= (logj x)/(logj k)