WorkSHEET 3.1 Exponential and logarithmic functions · · 2017-04-15WorkSHEET 3.1 Exponential and...
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Maths Quest Maths B Year 12 for Queensland 2e 1 WorkSHEET 3.1 Exponential and logarithmic functions Name: ____________________________ 1 Simplify: (a) ( ) ( ) ( ) 5 3 3 2 4 3 2 2 2 x y xy y x ´ (b) ( ) 4 2 5 2 1 2 1 4 6 6 2 1 2 3 4 ÷ ÷ ø ö ç ç è æ ´ ÷ ÷ ø ö ç ç è æ - - - - y x y x y x (a) ( ) ( ) ( ) 5 3 3 2 4 3 2 2 2 x y xy y x ´ 7 10 5 5 3 6 3 3 4 12 2 1 2 2 2 y x x y y x y x = ´ ´ ´ ´ ´ = (b) ( ) 4 2 5 2 1 2 1 4 6 6 2 1 2 3 4 ÷ ÷ ø ö ç ç è æ ´ ÷ ÷ ø ö ç ç è æ - - - - y x y x y x ( ) 9 4 10 2 2 3 2 1 2 3 9 2 1 2 y x y x y x y x = ´ = - - - -
Transcript of WorkSHEET 3.1 Exponential and logarithmic functions · · 2017-04-15WorkSHEET 3.1 Exponential and...
Maths Quest Maths B Year 12 for Queensland 2e 1
WorkSHEET 3.1 Exponential and logarithmic functions Name: ____________________________ 1 Simplify:
(a) ( ) ( )( )53
3243
222xyxyyx ´
(b)
( )4
25
21
21
46
6
21
23
4
÷÷
ø
ö
çç
è
æ
´÷÷
ø
ö
çç
è
æ
-
---
yx
yxyx
(a) ( ) ( )( )53
3243
222xyxyyx ´
710
553
633412
21
222
yx
xyyxyx
=
´´
´´´=
(b)
( )4
25
21
21
46
6
21
23
4
÷÷
ø
ö
çç
è
æ
´÷÷
ø
ö
çç
è
æ
-
---
yx
yxyx
( )
94
102
2321
239
21
2
yx
yxyxyx
=
´=
-
---
Maths Quest Maths B Year 12 for Queensland 2e 2
2 Simplify: (a) ( ) 2213 842 +- ÷´ nnn
(b) 23
32
916
278
÷øö
çèæ÷÷
øö
çèæ
-
(a) ( ) 2213 842 +- ÷´ nnn
( ) ( )
32
32
63433
232233
21
2222222
+
--
+-
+-
=
=
÷´=
÷´=
n
n
nnn
nnn
(b) 23
32
916
278
÷øö
çèæ÷÷
øö
çèæ
-
8
5
5
8
3
6
2
2
23
2
432
3
3
2332
32
32
32
32
=
=
÷=
÷÷ø
öççè
æ÷÷
÷ø
öççè
æ=
-
-
-
-
-
3 Simplify:
11 11 --
- -- xx
xx
11 11 --
- -- xx
xx Multiply both terms by !
!
( ) ( )( )( )
( )( )
( )( )( )
( )( )
( )12
1112112211
1111
11
2
2
32
2332
22
22
-=
---
=
---
=
--+--
=
-----
=
--
-=
xx
xxxxxxxx
xxxxxxxxxxxx
xx
xx
Maths Quest Maths B Year 12 for Queensland 2e 3
4 Solve for x: (a) ( ) 21log5 =-x
(b) 2491log -=÷øö
çèæx
(a) ( ) 21log5 =-x
2651 2
==-x
x
(b) 2491log -=÷øö
çèæx
77491
22
2
==
=
--
-
xx
x
5 Simplify:
(a) ÷øö
çèæ+x
x 1log2log4 22
(b) xx
3
63
loglog
(a) ÷øö
çèæ+x
x 1log2log4 22
0log2log2log2log422
12
21
2
=-=+= -
xxxx
(b) xx
3
63
loglog
12
log21log6log
log6
3
3
21
3
3
=
=
=
x
xx
x
6 Simplify:
(a) ÷øö
çèæ-641log381log2 23
(b) 2log8log9log 666 -+
(a) ÷øö
çèæ-641log381log2 23
26188
2log183log82log33log2
23
62
43
=+=
+=-= -
(b) 2log8log9log 666 -+
( )
26log26log36log
289log
6
26
6
6
===
=÷´=
Maths Quest Maths B Year 12 for Queensland 2e 4
7 If B
TaR +÷øö
çèæ= 10log , find a value for R, when
a = 30, T = 0.3 and B = 4.7.
7.67.42
7.4100log
7.43.030log
log
10
10
10
=+=
+=
+÷øö
çèæ=
+÷øö
çèæ=
RRR
R
BTaR
8 Solve for x in each of the following: (a) 51243 =x (b) 7293 52 =- x
(c) x
xx
-- = 3
2
255625
(a) 51243 =x
( )
5.196222296
932
===
=
xx
x
x
(b) 7293 52 =- x
8.05465233 652
-==-=-=-
xx
x
x
(c) x
xx
-- = 3
2
255625
( )( )
75.068
64455555
5
55
644
26
24
32
24
==
-=-=
=
=
--
--
-
-
xx
xx
xx
x
xx
x
xx
Maths Quest Maths B Year 12 for Queensland 2e 5
9 Solve for x in each of the following: (a) 0273632 =-´+ xx (b) ( ) 80215 4 =- x
(a) 0273632 =-´+ xx let xa 3=
( )( )
93or339or3
09302762
-==
-===+-=-+
xxaa
aaaa
x = 1 is the only possible solution (b) ( ) 80215 4 =- x
( )( )
( )
211or
21
221or2212or2)21(
162180215
444
4
4
-=
-=-=--=-
=-
=-
x
xxxxx
10 Solve for x in each of the following. Give answers exact to three decimal places. (a) ( ) 125.2 2 =- x (b) ( ) 406.0 3 <x ** Just do this question like its an equal sign **
(a) ( ) 125.2 2 =- x Take 10log of both sides:
( )
356.15.2log212log5.2log12log
2
12log5.2log212log5.2log
10
10
10
10
1010
102
10
-=
-=
=-
=-=-
x
x
x
x
x
(b) ( ) 406.0 3 <x
Take 10log of both sides:
( )
407.26.0log3
40log6.0log40log
3
40log6.0log340log6.0log
10
10
10
10
1010
103
10
->
>
>
<<
x
x
x
x
x
(÷ by neg.)
