Name: __________________________
Date: __________________________
MHF4U – In-Class Assignment – Exponential and Logarithmic Functions
T: ____/30
Show all steps for full marks.
1
Solve the equation
A
=
log z (26401-1)=4
8-0
z
2x tl
2x
2x
2
x
81
=
.
log 381
"
go
-
=
! 15=125
4
=
log 33
y
440g 33=4
I
4cL )
2*80
=
4
4=4
C- 31 )
If
Evaluate log − 31
be
negative
it's
log( x + 5)
log( x − 3)
Simplify
is the
If
,
cannot
even
can 't
it
argument
be
evaluated
since
the
,
log do
[1]
3
=
81
=
t I
[2]
34
=
-
31
be
,
it
then
is
I -31=-30
simplified
more
[1]
4
Solve for the variable. Show all steps for full marks. Write your answer in exact form.
log m =
log 48 − log12
2log 4
log YI
'
login
=
-
log
2.
logon
=
4
toga
210¥
I
logm
10¥ M
=
'
c
m=
To
.
[2]
5
5
Simplify:
s
=
=
s
( logs E )
slogs
=
[2]
1054
(log5 8−log5 2)
"
)
→
flagon
=
=
x
=
x
y
n
4
s
Page 1 of 4
argument
can't
Name: __________________________
6
The population of yeast cells in a culture grows exponentially from 125 to 4000 in 25 hours. What is its
doubling period in hours?
50=25
Mo (2)
M
I
-
-
25=125
( 2) ¥
I
4000
D=
D
2
=
Tzs
i. the
32=2
25=257
in
S
doubling period
culture
a
is
of
yeast
cells
population
5
IS
g
[2]
D=
S
4000
7
Date: __________________________
D
=
SD
25
=
Classify the statement as true or false. If false, change the second part to make it true.
If 2(3 x ) = 11, then x =
log 11
2 log 3
24×1=11
I
"
3
X
=
False
\
2
×=
log 3¥
=
log
't
log 3
logz
f-
log
3
[2]
8
After 90 days, a samplet of silver -110 decayed to 80% of its size. Determine the half-life of silver-110.
M
-
Mo
(f) Tn
90
81
100=1%8 (f)
I
90
0.08=4/5
'
.
,
the
is
half
24.7
logy 0.08=4,0
,
log 0.08
-
logo
=
's
h
qolog
=
=
[3]
n
logo
24.7
.
08
days
Page 2 of 4
life
days
or
of silver 110
-
Name: __________________________
9
Date: __________________________
Sketch the graph of the function. State the domain, range and the equation of the vertical asymptote.
Clearly plot key points and show your mapping rule.
1
x −1 + 1
2
f ( x) = 3log 2
log , 'z(
=3
x
2)
-
tl
{ XIXER , X > 2 }
Domain: ____________________
[1]
{ ylytr }
Range: _____________________
[1]
X
2
V.A.: _______________________
[1]
-
mapping
role :
EE ?
( 2×+2 ,3ytI )
( =/
D=
D :
VA:
)
× -2> o
×>2
unit up
2 to the
right
"
-
2x {
VA
at
r
i
I
z
y=2×
-
I
y
@ is
Yz
,
-
logs
,
(
"
-1
,3ytl )
'
e
(31*2)
)
q
i
z
!
!
si
6
s
foe
Hill
( i. o )
0,1
2×1-2
!
I
(6,4 )
(2,1 )
1,2
[5]
10
11
Systems of equations
1
2
If log a b = and logb a = 3x , find the value of x . Write your answer in exact form.
x
-6
log .ab=¥
laga =L
Iogbra 3×2
-_
tzlogba
3×2
=
logba
6×2
=
X
Gx
=
loaf
=
toga
×
2
=
*
6×2
x
-
X
=
o
X=
¥
{ logbfa=3X
?
toga
logb
10869
(6×-1)=0
X
-
O
6×-1=0
611--1
⇐
I
6
I
[4]
Page 3 of 4
[2]
,'
6.
-
x=2
Name: __________________________
Date: __________________________
11
Solve the equations simultaneously.
②
log y x − log x y = 0
①
2
j ¥+4
=
log
O
Cog H
③
log
'
=
x
(logy )
t
x'y
23
=
,
tog y
=3
y
=
z
3
=3
x'
y
s=
'
÷g×=I
z
log
t
x
z
log 2×2
2log 2 x + log 2 y = 3
-
log
④
'
.
:
x
=
Sff
logy
=
sub
④
"
in to
③
¥: :
"
.
Ey
8
Ts
=
=
=
2-
y
y
'
'
f
:÷
x
=
×=
.
54
2
y
y
(2,2 )
[6]
Page 4 of 4
Name: __________________________
Date: __________________________
11
Solve the equations simultaneously.
log y x − log x y = 0
2log 2 x + log 2 y = 3
[6]
Page 4 of 4