Further Pure Mathematics

1. Further Pure Mathematics Notes
1.1 Logarithmic Functions and Indices>1.2 The Quadratic Function>1.3 Identities and Inequalities>1.4 Graphs>1.5 Series>1.6 The Binomial Series>1.7 Scalar and Vector Quantities>1.8 Rectangular Cartesian Coordinates>1.9 Calculus>1.10 Trigonometry>

For example log₂32 = 5 means that 25 = 32

In words, you would say ‘the logarithm of 32, to base 2, is 5

To remove log, solve for x:

On one side: use concept of log to remove
1. E.g. log₂x = 4 → x = 2⁴ = 16
On two sides: use change of base law (rule 8 above), to make both logarithms have the same base, then cancel out log
When solving log in quadratic: make “log a b = x” to solve as a normal quadratic, then replace values of “x” to equal “log a b”

Natural log

log a = ln

Always keep final answer always in ln