Grade 12 Maths · Functions · Paper 1

Logarithms Grade 12

Real Logarithms past paper questions and answers from 2023 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 22 past paper questions
skills: 5 skills
videos: 5 videos

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Question 6.1 · May/June 2025 · Paper 1 · National (DBE) · 4 marks

The graphs of

f (x) = p^{x} + q

and

g (x) = m x + c

are drawn below.

A (3; 4)

is the point of intersection of

f

and

g

B (0; - 3)

is the y-intercept of

f

. E is the x-intercept of

g

6.1 Calculate the values of

p

and

q

.(4)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Logarithms skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Logarithms Grade 12 questions and answers

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4. Question 1.1.3 · May/June 2025 · Paper 1 · National (DBE) · 3 marks
1.1 Solve for $x$ :
1.1.3 $2^{x + 4} + 2^{x} = 8704$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Factorise the common exponential term $2^{x} (16 + 1) = 8704$
  1 mark · Take out a common power
2. ✓
  Simplify to a single exponential equation $2^{x} (17) = 8704$
  $2^{x} = 512$
  1 mark · Solve a linear equation
3. ✓
  Solve for x $2^{x} = 2^{9}$
  $x = 9$
  1 mark · Solve an exponential equation
5. Question 4.1 · March 2025 · Provincial · 2 marks
The diagram below shows the graph of $k (x) = a^{x}$ . Point $B (3; 3 \frac{3}{8})$ lies on $k$ .
4.1 Show that $a = \frac{3}{2}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute point B into equation $3 \frac{3}{8} = a^{3}$
  $\frac{27}{8} = a^{3}$
  1 mark · Find equation of exponential graph
2. ✓
  Solve for a $a = 3 \frac{27}{8}$
  $a = \frac{3}{2}$
  1 mark · Solve an equation with rational exponents
6. Question 4.2.1 · March 2025 · Provincial · 2 marks
4.2 Consider $g (x) = (\frac{1}{3})^{x}$ .
4.2.1 Determine the equation of $g^{- 1}$ in the form $y = ...$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Swap x and y $x = (\frac{1}{3})^{y}$
  1 mark · Find the equation of an inverse
2. ✓
  Write in log form $y = lo g_{\frac{1}{3}} x$ or $y = - lo g_{3} x$
  1 mark · Convert between log and exponential form
7. Question 5.2.1 · September 2024 · Paper 1 · Provincial · 2 marks
5.2 The graph of $h (x) = a^{x}$ is sketched below. $A (- 1; \frac{1}{2})$ is a point on the graph of h.
5.2.1 Substantiate why the coordinates of Q, the y-intercept of h, are (0; 1).(2)
Show the memo (2 ticks)Memo
1. ✓
  Substantiate x=0 $x = 0$
  1 mark · Find the y-intercept
2. ✓
  Value of h(0) $h (0) = 1$
  1 mark · Find the y-intercept
8. Question 6.1 · March 2023 · Provincial · 2 marks
The diagram shows the graph $f (x) = a^{x}$ . Point $B (3; 3 \frac{3}{8})$ lies on $f$ .
6.1 Show that $a = \frac{3}{2}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute point B $3 \frac{3}{8} = \frac{27}{8}$
  $\frac{27}{8} = a^{3}$
  1 mark · Find equation of exponential graph
2. ✓
  Solve for a $a = 3 \frac{27}{8} = \frac{3}{2}$
  1 mark · Solve an equation with rational exponents

Logarithms Grade 12 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Exponential Equation Given Graph | Grade 11 FunctionsKevinmathscience

Writing Logarithmic Equations In Exponential FormThe Organic Chemistry Tutor

8) Inverse equations | Many examplesKevinmathscience

6) Inverse of exponential | Part 1Kevinmathscience

Number of Payments | Gr 12 Financial MathsKevinmathscience

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