Logarithmic and exponential functions — IGCSE Mathematics - Additional (0606) questions by topic
Logarithmic and exponential functions cover sketching a function such as f(x) equals 2 times e to the negative x plus 3 alongside its inverse, writing down the set of values for which a logarithm exists, solving an equation combining a logarithm base x with a common logarithm, and finding exact intersection points of two logarithmic curves. Find, solve, draw and state are the top command words, with solve tasks needing exact rather than decimal answers.
This page holds 5 real questions worth between 4 and 8 marks, all from 2025 papers. Because sketches and exact-form solutions are both graded closely against the mark scheme, submit your sketches and algebraic answers for instant marking to check domain restrictions and exact simplification are both handled correctly.
May–June 2025, Paper 11
Write down the set of values of x for which log5 (12x − 4) exists.
Answer this question and get it marked →May–June 2025, Paper 13
Solve the equation 2 / (logx 10) - lg(x + 4) = lg 2 for x 0.
Answer this question and get it marked →Find the x-coordinates of the points of intersection of the following curves. y = 4 ln x and y = 5 - 3 / ln(x^2) Give your answers in exact form.
Answer this question and get it marked →May–June 2025, Paper 21
The function f is defined by f(x) = 2e^(−x) + 3 for x ∈ ℝ. On the axes, sketch the graph of y = f(x) and hence, on the same axes, sketch the graph of y = f^(−1)(x). Show clearly:…
Answer this question and get it marked →May–June 2025, Paper 23
Solve the equation 64^(x + 1/3) + 2^(3x) − 3 = 0.
Answer this question and get it marked →Other IGCSE Mathematics - Additional topics
- Differentiation (9)
- Series (8)
- Functions (5)
- Trigonometry (5)
- Permutations and combinations (5)
- Integration (5)