exponential and logarithmic 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 growth

f(x)=a*b^x

a>0 and b>0

exponential decay

f(x)=a*b^x

a>0 and b<0

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 any base except 10

written as logd to the x

to the base 10

also called common

written as log to the x

to the base e

also called natural

witten as ln x

THERE ARE TWO MAIN PROPERTIES OF LOGARITHMIC FUNCTIONS

expanding logarithmic functions

the 3 properties of expanding:

product property

logb mn = logb m + logb n

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

quotient property

logb m/n = logb m - logb n

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

power prperty

logb m^ n = n logb m

example:
log6 125=
3 log6 5

condensing logarithmic functions

the 3 properties of condensing:

product property

logb m + logb n = logb mn

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

quotient property

logb m - logb n = logb m/n

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

power property

n logb mn = logb m^n

example:
3 log6 5=
log6 125