Exponential and Logarithmic Functions practice questions

Secondary 3 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise exponential and logarithmic functions free

What this topic covers

Worked examples

Example 1

Solve 3⋅32x+8⋅3x−3=03 \cdot 3^{2x} + 8 \cdot 3^x - 3 = 0.
Show the worked solution
  • $3 \cdot 3^{2x} + 8 \cdot 3^x - 3 = 0$
  • $\text{Let } y = 3^x \quad \scriptsize\textit{substitution}$
  • $3y^2 + 8y - 3 = 0$
  • $(3y - 1)(y + 3) = 0$
  • $y = \frac{1}{3} \text{ or } y = -3$
  • $\text{Since } 3^x > 0, \text{ reject } y = -3$
  • $3^x = \frac{1}{3}$
  • $3^x = 3^{-1}$

Answer: −1-1

Example 2

Without using a calculator, simplify log⁡36+log⁡392\log_3 6 + \log_3 \frac{9}{2}.
Show the worked solution
  • $\log_3 6 + \log_3 \frac{9}{2}$
  • $= \log_3 \left(6 \times \frac{9}{2}\right) \quad \scriptsize\textit{product law}$
  • $= \log_3 27$
  • $= \log_3 3^3$
  • $= 3$

Answer: 33

Example 3

Solve log⁡7(x+32)−log⁡7(x−4)=1\log_{7}(x + 32) - \log_{7}(x - 4) = 1.
Show the worked solution
  • $\log_{7}(x + 32) - \log_{7}(x - 4) = 1$
  • $\log_{7} \frac{x + 32}{x - 4} = 1 \quad \scriptsize\textit{quotient law}$
  • $\frac{x + 32}{x - 4} = 7^{1} = 7$
  • $x + 32 = 7(x - 4)$
  • $x + 32 = 7x - 28$
  • $28 + 32 = 6x$
  • $60 = 6x$
  • $x = 10$

Answer: 1010

Questions parents ask

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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