Logarithms: The Complete Grade 12 Guide — Worksheet & Memo

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Grade 12 · Functions

Logarithms: The Complete Grade 12 Guide

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)4
C)16
D)2
1.2
log 100 = …
(1)
A)2
B)10
C)100
D)1 000
1.3
log a + log b = …
(1)
A)log(ab)
B)log(a + b)
C)log a × log b
D)log alog b
1.4
log 200 − log 2 = …
(1)
A)2
B)log 198
C)100
D)1
1.5
log(x³) = …
(1)
A)3 log x
B)(log x)³
C)log 3x
D)log x3
1.6
If log₃x = 4, then x = …
(1)
A)81
B)12
C)64
D)1,32
1.7
log 1 = …
(1)
A)0
B)1
C)10
D)undefined
1.8
log(−5) is …
(1)
A)undefined
B)−log 5
C)0
D)5
1.9
Using the change-of-base rule, log₅20 = …
(1)
A)log 20log 5
B)log 5log 20
C)log 20 − log 5
D)log 4
1.10
Solve for x, correct to TWO decimal places: 2^x = 20
(1)
A)4,32
B)10
C)1,30
D)0,30

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
log₂ (x + 3) + log₂ (x − 3) = 4
(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
Simplify: 2 log 5 + log 4
(4)
3.2
Simplify: log 50 − log 5
(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.