Download Worksheet 7.1

Maths Quest Maths B Year 11 for Queensland
WorkSHEET 7.1
1

3

Write in simplest index notation:
2a
n2
b3
(a
2a

4
2 ab
n2
b

2
3 6

6
4
2
(3a n b 2 n 2 ) 3  4(ab1n ) 2
(a 3 b 3 ) 4  ( 2a 4 b 3 ) 3

2 ab  2
3 3
b )  ( 2a b )
3

 27 a 3n b 6 n 6  4a 2 b 22 n
64a 6 n 12b18
 27b 4 n 22

16a 3n 10

Write in simplest index notation:
3
2
a 6 b 4  64a 3b 9

8a 6 b18
8a 3
 5
b
9 2
(3a n b 2 n  2 ) 3  4(ab1 n ) 2
3

3 3
8a b
2
(a 3b 2 ) 2  (4ab 3 ) 3
8 a 3b 9
(a b )  (4ab )
2 2
1
Exponential and logarithmic functions
Name: ______________________
Write in simplest index notation:
3
Chapter 7 Exponential and Logarithmic Functions WorkSHEET 7.1

2 2

a
12
b
3
4
2
2

2
 2 2a12b 9
2a  2 b 4
2a 2
 7
b
4
Write in simplest index notation:
(a
(a
2n
3n
b )
3
5
 (a b )
ab 
2n 2
3n
3
1
5 2
b )  (a b )
2n
3n
3n
ab 
2 n 2
1
2
3 n 5 n
 6 n 92 n
a b a 2 b 2

a 2 b 4 n



a
3 n
b
9 n
4
3n
4
a b
a b
1
2




5 n
4
1 2 n
1

1
5n
a4b
22 n
4
 1 4
  5n 22n 
a b 
2
Maths Quest Maths B Year 11 for Queensland
5
Chapter 7 Exponential and Logarithmic Functions WorkSHEET 7.1
Write in simplest index notation:
5
1024 2  8
32 0.6
2

3
5
1024 2  8
32 0.6

2
2
3
2

 10 2
 2   2 3  3

3

2 5 5

20

2 5 2

2
1
5




2
5
3
5
2
2 8
3
6
Solve for x in the equation 2 2 x 3  64 x  0
2 2 x  3  64 x  0
2 2 x  3  64 x
2 2 x  3  ( 26 ) x
1
2x  3  6x
 3  4x
x
7
Solve for x in the equation 81 
1
0
27 x 1
81 
3
4
1
0
27 x 1
81 
34 
1
27 x 1
1
3 
3 x 1
3 4  3 3 x 3
4  3 x  3
3 x  7
1
x  2
3
8
Solve for x in the equation 5 2 x  4(5 x )  5  0
1
1
1
52 x  4(5 x )  5  0
let y  5 x
y2  4 y  5  0
 y  5 y  1  0
y  5 or y  1
5 x  5 or 5 x  1
x = 1 is only feasible solution
1
1
Maths Quest Maths B Year 11 for Queensland
9
Chapter 7 Exponential and Logarithmic Functions WorkSHEET 7.1
For the graph: y  3 2 x  1 , state the:
(a) asymptote
y  32 x  1
(a) Asymptote y  1
1
(b) y-intercept
(b) y-intercept: when x = 0, y  30  1  0
1
(c) domain
(c) Domain x : x  R
1
(d) range
10
3
(d) Range y : y  1
x
1
x
1
For the graph: y  6    , state the:
2
(a) asymptote
1
y  6     6  2x
2
(a) Asymptote y = 6
(b) y-intercept
(b) y-intercept: when x  0, y  6  20  5
1
(c) domain
(c) Domain x : x  R
1
(d) range
(d) Range y : y  6
1
1