Grade 10 Maths · Algebra

Solve an exponential equation

Solve an equation with the unknown in the power by making the bases the same and equating the powers (for example 2ˣ = 2³, so x = 3).

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Exponential Equations grade 10Kevinmathscience

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Exponential Equation Grade 10 ExamKevinmathscience

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Question 4.4 · November 2024 · Paper 1 · National (DBE) · 3 marks

Given:

f (x) = a^{x} - 1

for

a > 0

B (2; \frac{- 5}{9})

is a point on

f

4.4 It is further given that

C

is a point on

f

y = \frac{19}{8}

. Determine the coordinates of

C^{'}

, the image of

C

, when

C

is reflected about the line

y = x

.(3)

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

More past paper questions: solve an exponential equation

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3. Question 1.1.4 · November 2024 · Paper 1 · National (DBE) · 5 marks
1.1 Solve for $x$ :
1.1.4 $2^{2 x} - 2^{x + 2} - 32 = 0$ (5)
Show the memo (4 ticks)Memo
1. ✓
  Expand exponential term $2^{2 x} - 2^{2} \cdot 2^{x} - 32 = 0$
  $2^{2 x} - 4 \cdot 2^{x} - 32 = 0$
  1 mark · Use the laws of exponents
2. ✓
  Factorise $(2^{x} - 8) (2^{x} + 4) = 0$
  1 mark · Factorise a trinomial
3. ✓
  Solve for the exponential term $2^{x} = 8$ or $2^{x} = - 4$
  2 marks · Solve an exponential equation
4. ✓
  Solve for x $2^{x} = 2^{3}$
  $x = 3$
  1 mark · Solve an exponential equation
4. Question 1.1.4 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for x:
1.1.4 $5^{2 x} - 5^{x} = 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Common factor $5^{x} (5^{x} - 1) = 0$
  2 marks · Take out a common power
2. ✓
  Rejecting $5^{x} = 0$ $5^{x} \neq = 0$ or $5^{x} = 1$
  1 mark · Solve an exponential equation
3. ✓
  Solve for x $x = 0$
  1 mark · Solve an exponential equation
5. 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
6. Question 2.2.2 · March 2025 · Provincial · 3 marks
2.2 Solve for $x$ , without using a calculator:
2.2.2 $(5^{x} - 125) (5^{x} + 1) = 0$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Both equations after transposing $5^{x} = 125$ or $5^{x} = - 1$
  1 mark · Solve a quadratic by factorising
2. ✓
  Same base and no solution $5^{x} = 5^{3}$ ; $5^{x} = - 1$ has no solution
  1 mark · Solve an exponential equation
3. ✓
  Answer $x = 3$
  1 mark · Solve an exponential equation

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