What you’ll learn4 learning objectivesChoose one objective for a focused lesson, or study the complete topic.3.2.1Log laws• understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base)Syllabus objective3.2.2Exponential and ln• understand the definition and properties of ex and ln x, including their relationship as inverse functions and their graphs Including knowledge of the graph of y = ekx for both positive and negative values of k.Syllabus objective3.2.3Log equations• use logarithms to solve equations and inequalities in which the unknown appears in indices e.g. 25x 1, 32 5<x31# -, 34xx 12 1= -+.Syllabus objective3.2.4Linearising relationships• use logarithms to transform a given relationship to linear form, and hence determine unknown constants by considering the gradient and/or intercept. e.g. y = kxn gives ln y = ln k + n ln x which is linear in ln x and ln y. y = k (ax) gives ln y = ln k + x ln a which is linear in x and ln y.Syllabus objective