Full Logs & Exponentials Notes — Cambridge IGCSE Additional Mathematics 0606

Topic 6: Logarithmic and exponential functions. Built from the 2025–2027 Cambridge IGCSE Additional Mathematics 0606 syllabus.

What this chapter must train

By the end, students should be able to:

• Understand simple properties and graphs of logarithmic and exponential functions.
• Use (e^x) and (ln x).
• Understand that (e^x) and (ln x) are inverse functions.
• Understand asymptotes of exponential and logarithmic graphs.
• Use laws of logarithms.
• Use change of base.
• Solve equations of the form (a^x=b).

1. Exponential functions

An exponential function has the variable in the power.

Examples:

$$ y=2^x $$

$$ y=3e^x $$

$$ y=ke^{nx}+a $$

Key idea

Exponential growth increases by multiplication, not addition.