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 :(a^b) ^x = a^b*x

eg:(2²)² = 2^2*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 _bx^y= y

if a base is rased to a power and log is the same base the power

• log ^{logb x} = x

http://www.mathwords.com/l/logarithm_rules.htm
http://www.sosmath.com/algebra/logs/log4/log44/log44.html
http://www.purplemath.com/modules/logrules.htm
http://www.youtube.com/watch?v=PupNgv49_WY

the next scribe is Kale