exponential and logarithmic functions

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exponential and logarithmic functions

3.3 properties of logarithmic functions

THERE ARE TWO MAIN PROPERTIES OF LOGARITHMIC FUNCTIONS

condensing logarithmic functions

the 3 properties of condensing:

power property

n logb mn = logb m^n

example: 3 log6 5= log6 125

logb m - logb n = logb m/n

example: ln (x^2+5)-x= ln x+5/x

logb m + logb n = logb mn

example: log 8 + log x + 4 log y= log(8xy^4)

expanding logarithmic functions

the 3 properties of expanding:

power prperty

logb m^ n = n logb m

example: log6 125= 3 log6 5

quotient property

logb m/n = logb m - logb n

example: ln x+5/x= ln (x^2+5)-x

product property

logb mn = logb m + logb n

example: log(8xy^4)= log 8 + log x + 4 log y

3.2 logarithmic functions

it follows a^x

for x>0, a>0, and a is not equal to 1 y=logax if and only if x=a^y

fro example: log base 3 of 9 is equivalent to 3 to the power of 2

THERE ARE THREE TYPES OF LOGARITHMIC FUNCTIONS:

to the base e

also called natural

witten as ln x

to the base 10

also called common

written as log to the x

to any base except 10

written as logd to the x

3.1 exponential functions

the exponential function f with base a is denoted by f(x)=a^x

f(x)=a*b^2, where a is a non zero, b is positive, and b is not equal to 1. the constant a is the initial value and b is the base

THERE ARE TWO TYPES OF EXPONENTIAL FUNCTIONS:

exponential decay

a>0 and b<0

exponential growth

f(x)=a*b^x

a>0 and b>0