によって Maryam Alameri 6年前.
1501
もっと見る
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)
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
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
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