A2M3L8­SB WhatPower Function.notebook
February 01, 2016
The “WhatPower” Function
Do Now:
1. Evaluate each expression. The first two have beencompleted for you.
a)
What power of 2 is 8? 3
b)
What power of 3 is 9 2
A2M3L8­SB WhatPower Function.notebook
February 01, 2016
___________________
c)
What power of 6 is 36?
___________________
d)
What power of 2 is 32?
e)
___________________
What power of 10 is 1000?
What power of 10 is 1,000,000?
What power of 100 is 1,000,000?
h) What power of 4 is 64?
i)
What power of 2 is 64?
A2M3L8­SB WhatPower Function.notebook
j)
k)
l)
m)
n)
o)
p)
February 01, 2016
A2M3L8­SB WhatPower Function.notebook
February 01, 2016
Write a definition for the function where
,
is a number.
The value of
is the number you need to
raise to in order to get . That is if , then WhatPower of b is X?
L
A2M3L8­SB WhatPower Function.notebook
February 01, 2016
Evaluate the following expressions, and justify your answers.
A2M3L8­SB WhatPower Function.notebook
February 01, 2016
Describe the allowable values of in the expression When can we define a function:
? Explain how you know. If b=0 or b=1 then the expression does not make sense. If b<0 , then the expression makes sense for some values of X but not for others, so we cannot define a function if b<0. Thus, we can define the function:
f(x) = if b > 0 and b 1.
WhatPower function is a mathematical term called logarithm.
.
A2M3L8­SB WhatPower Function.notebook
February 01, 2016
Definition of the Logarithm Base b
Characteristics
If three numbers L,b and X
with 0 < b < 1 or b>1
If
are related by If
, then
L is the logarithm base b of x, and we write
. and
. ,
and
, then
.
Logarithm
Examples
Non‐Examples Rewrite in the form:
Rewrite in the form:
Rewrite in the form: A2M3L8­SB WhatPower Function.notebook
February 01, 2016
Is log5(25) a valid example?
Is log5(­25)a valid example?
Is log5(0)a valid example?
What are some characteristics of Logarithms?
Evaluate:
______
______
______
______
______
______
A2M3L8­SB WhatPower Function.notebook
Compute the value of each logarithm.
Verify your answers using an exponential statement. Homework
February 01, 2016
A2M3L8­SB WhatPower Function.notebook
February 01, 2016