Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

Indices & Logarithms

14 min read

The laws of indices, logarithms as the inverse of powers, the log laws, and solving exponential equations.

Logarithms undo exponentials, turning awkward powers into manageable sums.

Laws of indices

$a^m a^n = a^{m+n},\quad \frac{a^m}{a^n} = a^{m-n},\quad (a^m)^n = a^{mn},\quad a^0 = 1,\quad a^{-n} = \frac{1}{a^n},\quad a^{1/n} = \sqrt[n]{a}$

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.

Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

14 min read

The laws of indices, logarithms as the inverse of powers, the log laws, and solving exponential equations.

Logarithms undo exponentials, turning awkward powers into manageable sums.

$a^m a^n = a^{m+n},\quad \frac{a^m}{a^n} = a^{m-n},\quad (a^m)^n = a^{mn},\quad a^0 = 1,\quad a^{-n} = \frac{1}{a^n},\quad a^{1/n} = \sqrt[n]{a}$

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.