Logarithms: Definition, Graphs and Solving for n — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 12 · Functions and Graphs

Logarithms: Definition, Graphs and Solving for n

EXAM-STYLE CLASS TEST

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 36

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
log₂8 = …
(1)
A)3
B)2
C)4
D)16
1.2
log 100 = …
(1)
A)100
B)2
C)1 000
D)10
1.3
The inverse of y = 2^x is …
(1)
A)y = log₂ x
B)y = 2^−x
C)y = x²
D)y = log_x 2
1.4
The graph of y = log₂ x passes through …
(1)
A)(0 ; 1)
B)(1 ; 0)
C)(2 ; 0)
D)(0 ; 2)
1.5
The graph of y = log_1/2 x …
(1)
A)increases from left to right
B)decreases from left to right
C)is a straight line
D)is defined for x < 0
1.6
If log₃x = 4, then x = …
(1)
A)1,32
B)12
C)81
D)64
1.7
log 1 = …
(1)
A)10
B)undefined
C)0
D)1
1.8
log(−5) is …
(1)
A)5
B)undefined
C)0
D)−log 5
1.9
R5 000 grows to R10 000 at 8% p.a. compounded annually. The number of years n is given by …
(1)
A)n = log_1,08 2
B)n = log₂ 1,08
C)n = 2 ÷ 1,08
D)n = 1,08²
1.10
Solve for x, correct to TWO decimal places: 2^x = 20
(1)
A)10
B)0,30
C)1,30
D)4,32

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[13 MARKS]

Solve for x. Show ALL your working.

2.1
R5 000 is invested at 9% p.a. compounded annually. Solve 5 000(1,09)ⁿ = 12 000 to find how long it takes to grow to R12 000, correct to TWO decimal places, and interpret your answer.
(6)
2.2
3^x = 20, correct to TWO decimal places
(4)
2.3
log_x 81 = 4
(3)

Question 3

[13 MARKS]

Answer the questions below WITHOUT the use of a calculator.

3.1
Write log₃ 81 = 4 in exponential form, and hence determine log₃ 1/9.
(4)
3.2
Determine log₂ 32 + log₅ 1.
(3)
3.3
Write down the equation of the inverse of f(x) = 2^x in the form y = …
(3)
3.4
Write down the domain of y = log₂ x, and explain why.
(3)

TOTAL: 36 marks

This question paper consists of 3 questions.