Maths › Equations › Exponentials and logarithms

Exponentials and logarithms formulae

The 5 results the exponentials and logarithms notes display, each with the conditions it needs to be true and a link to the lesson that states it. The formulae booklet prints none of them, so every one is yours to carry into the examination in your head.

Year 12 · 2 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

2 lessons

Exponential functions and e

\text{gradient of } e^{kx} = ke^{kx}

NOT IN THE BOOKLET: LEARN ITConditionsAll x; no restriction.

Logarithms and their laws

x = a^{n} \iff n = \text{log}_{a} x

NOT IN THE BOOKLET: LEARN ITConditionsa > 0, a ≠ 1 and x > 0.

\text{log}_{a} x + \text{log}_{a} y = \text{log}_{a} xy

NOT IN THE BOOKLET: LEARN ITConditionsa > 0, a ≠ 1, x > 0 and y > 0.

\text{log}_{a} x − \text{log}_{a} y = \text{log}_{a} \frac{x}{y}

NOT IN THE BOOKLET: LEARN ITConditionsa > 0, a ≠ 1, x > 0 and y > 0.

k \text{log}_{a} x = \text{log}_{a} x^{k}

NOT IN THE BOOKLET: LEARN ITConditionsa > 0, a ≠ 1 and x > 0.

Every formula in the library is indexed by unit on the equation index, and the exponentials and logarithms notes are where these results are derived and used. The 5 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Trigonometry formulae · Differentiation formulae