Grade 12 Maths · Functions

Convert between log and exponential form

Switch between log form and power form (for example log₂ 8 = 3 means 2³ = 8).

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Writing Logarithmic Equations In Exponential FormThe Organic Chemistry Tutor

Introduction to Logarithms (1 of 2: Definition)Eddie Woo

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Question 5.2 · May/June 2024 · Paper 1 · National (DBE) · 2 marks

In the diagram, the graphs of

f (x) = lo g_{a} x

and

g

are drawn. Graph

g

is the reflection of

f

in the line

y = x

. Graph

f

passes through the point P

(4; 2)

. Q is the

x

-intercept of

f

and R is the

y

-intercept of

g

5.2 Show that

a = 2

.(2)

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

More past paper questions: convert between log and exponential form

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3. Question 5.3.2 · September 2024 · Paper 1 · Provincial · 2 marks
5.3 The price $(p),$ in Rands per unit, of EACH item in a consignment of q items, is given by $p = lo g (10 + \frac{q}{2})$
5.3.2 Determine the number of items in the consignment when the price of each item is R2.(2)
Show the memo (2 ticks)Memo
1. ✓
  Exponential equation $1 0^{2} = 10 + \frac{q}{2}$
  1 mark · Convert between log and exponential form
2. ✓
  Answer $q = 180$
  1 mark · Convert between log and exponential form
4. 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
5. Question 6.4 · March 2023 · Provincial · 2 marks
The diagram shows the graph $f (x) = a^{x}$ . Point $B (3; 3 \frac{3}{8})$ lies on $f$ .
6.4 Write down the equation of $g$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Swap x and y $x = (\frac{3}{2})^{y}$
  1 mark · Find the equation of an inverse
2. ✓
  Equation of g $g (x) = lo g_{\frac{3}{2}} x$
  1 mark · Convert between log and exponential form

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