MathAmigo

Exponential and Logarithmic Functions

Secondary 3 Additional Math practice

Start free

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 22x−1=02^{2x} - 1 = 0.
Show the worked solution
  • 22x−1=02^{2x} - 1 = 0
  • Let y=2xsubstitution\text{Let } y = 2^x \quad \scriptsize\textit{substitution}
  • y2−1=0y^2 - 1 = 0
  • (y−1)(y+1)=0(y - 1)(y + 1) = 0
  • y=1 or y=−1y = 1 \text{ or } y = -1
  • Since 2x>0, reject y=−1\text{Since } 2^x > 0, \text{ reject } y = -1
  • 2x=12^x = 1
  • 2x=202^x = 2^0

Answer: 00

Example 2

Without using a calculator, simplify lg⁡100+lg⁡100\lg 100 + \lg 100.
Show the worked solution
  • lg⁡100+lg⁡100\lg 100 + \lg 100
  • =lg⁡(100×100)product law= \lg(100 \times 100) \quad \scriptsize\textit{product law}
  • =lg⁡10 000= \lg 10\,000
  • =lg⁡104= \lg 10^{4}
  • =4= 4

Answer: 44

Example 3

Solve 2lg⁡x−lg⁡(x+2000)=22\lg x - \lg(x + 2000) = 2.
Show the worked solution
  • 2lg⁡x−lg⁡(x+2000)=22\lg x - \lg(x + 2000) = 2
  • lg⁡x2−lg⁡(x+2000)=2power law\lg x^2 - \lg(x + 2000) = 2 \quad \scriptsize\textit{power law}
  • lg⁡x2x+2000=2quotient law\lg \frac{x^2}{x + 2000} = 2 \quad \scriptsize\textit{quotient law}
  • x2x+2000=102\frac{x^2}{x + 2000} = 10^{2}
  • =100= 100
  • x2=100(x+2000)x^2 = 100(x + 2000)
  • x2−100x−200 000=0x^2 - 100x - 200\,000 = 0
  • (x−500)(x+400)=0(x - 500)(x + 400) = 0

Answer: 500500

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

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.

Other Secondary 3 Additional Math topics