MHF4U1: Unit#8 – Lesson #1
Name:
8.1 Logarithmic Function
Warm-up: Simplify the following
a) 2𝑥+1 ∙ 22𝑥−3
b)
43𝑥−3
4 𝑥+1
c) (42𝑥+1 )5
d)
1
3𝑥−1
e) (456−32𝑥−45 )0
2. State all the exponent rules that you have learned so far
Lesson:
1. How would the graph of the inverse of the exponential functions (𝒚
a)
𝑏 >1
𝑦 = 𝑏𝑥
Domain
Range
Intercepts
Asymptote
End Behaviour
x  , y 
x  , y 
(use the same grids)
0 < 𝑏 < 1
b)
𝑏 >1
Inverse 𝑦 = 𝑏 𝑥
x  , y 
x  , y 
= 𝒃𝒙 ) look like?
𝑦 = 𝑏𝑥
0 < 𝑏 < 1
Inverse 𝑦 = 𝑏 𝑥
x  , y 
x  , y 
The name of the inverse functions is __________________________
The logarithmic function is a reflection of the exponential function on the line y  x .
Exponential function
y  ax
Logaritmic function
x  , y 
x  , y 
MHF4U1: Unit#8 – Lesson #1
Name:
2. To get the equation of the logarithmic function, you need to find the inverse function of y  b x . Determine the
inverse function of y  2 x .
So Exponential form
x2
and
Logarithmic form
y  log 2 x
y
Definition
The exponential function
x  b y can be written as the logarithmic function y  log b x , where 𝑏 > 0 and b  1(same
restrictions like the exponential function).
The logarithm function
x  b y is the inverse of the exponential function y  b . Hence,
x
x  a y  y  log a x
Example: y  log2 8 since the exponent required on 2 (the base) to give 8 (the value of x) is 3.
y 3
3. Write each exponential equation in Logarithmic form.
1
c) 2  3 
b) 9 2  3
a) 5 3  125
1
8
4. Write each logarithmic equation in exponential form.
a) log 4 64  3
b) log 6
1
 1
6
c) log 3 1  0
5. Evaluate
a) log 3 81
b) log 1
2
Homework: Pg. 451 #1ab, 2-3, 5-10
2
c)
log5 5
d)
log 3 1
e)
log 6 0