## Saturday, April 18, 2009

### Relationship between exponent and logarithm

Hi, this is Ale, I am sorry for the delay in posting. On Friday we learned the relationship between an exponent and logarithm. In order to understand how logarithm work we need to remember exponential function because a logarithm is a inverse of an exponential function.
What a function does its inverse undoes it. We also have to remember that the exponential function is of form

Where b is the base a is the exponent or the input in case of a function and x is the power.The most important thing we learned is that the logarithm is an exponent. With The famous formula

the exponential function turns the input into power so its inverse which is a logarithm will turn the power exponent

for example if 42 = 16, exponent then its inverse will be log416 = 2

We also have to know that every exponent function has a base of 1

W

http://www.themathpage.com/aPreCalc/logarithmic-exponential-functions.htm

exponential function has x as asymptote but its inverse which logarithm has y as asymptote

We also learned logarithmic laws or rules. As logarithm is an exponent. many law applied to exponent are also used for logarithm

Product law

for exponent :(ab) x = ab*x

eg:(22)2 = 22*2 = 24
• log b MN = log b M*log b

Eg: log 2(8*16) = log 2 8*log 2 16
3 + 4 = 7
• log b (M/N) = log b M-log b N
Eg: log 2(32/138) = log 2 32*log 2 13
5 - 7 = -2
The power law
• log bM k = klog bM
eg : log 285 = 5log 28

Special cases

If the base and the power are the same the result is the same

• log bxy= y
if a base is rased to a power and log is the same base the power

• log logb x = x
http://www.purplemath.com/modules/logrules.htm