Content PageCommon Logarithm

IntroductionHistory

Henry Briggs Calculators

Change of Base LawGraph

Natural LogarithmIntroductionHistoryGraph

Common Logarithm - IntroductionCommon Logarithms are logarithms to base

10

Commonly abbreviated as lgHence, for example

Common Logarithm - HistorySometimes called Briggsian LogarithmNamed after Henry Briggs, a 17th century

mathematicianIn calculators, when you press logIt is actually log10 or lgThis is because base 10 logarithms are useful

for computationsEngineers often used log to represent log10 Since engineers programmed calculators, log

became log10

Common Logarithm - HistoryHowever, this is extremely misleading So we have to take note in case we make

such a mistake by confusing log10 with logWe often need to make use of logarithms of

non-10 basesHence, we will briefly cover the Change of

Base Law

Common Logarithm – Change of Base LawIf a, b and c are positive numbers and a 1, c 1

This law is used to manipulate bases, and hence allow us to overcome to problem of common bases in calculators

Common Logarithm – Change of Base LawThis law can be used to convert common

logarithms to natural logarithms, and vice versa

log10N = logeN / loge10

= (ln N) / (ln 10) = (ln N) / 2.30258 = 0.4343 × ln N

Natural Logarithms- Introduction

• Beside base 10, another important base is e• where e= 2.71828 (5 d.p)• Logarithms to base e are called natural

logarithms

• “log e” is often abbreviated as “ln”

Natural Logarithms- IntroductionNatural logarithms may also be evaluated

using the “ln” button on a scientific calculator.

By definition,

ln Y = X <-> Y = ex

Natural Logarithms- HistoryA mathematics teacher, John Speidell,

compiled a table on the natural logarithm in 1619.

The first mention of the natural logarithm was by Nicholas Mercator in his work Logarithmotechnia published year 1668.

It was formerly known as the hyperbolic logarithm.

Natural Logarithms- Examples• 1. ln p = 3 2. loge p = 3 3. p = e³

• 1. e2x = k 2. 2x = loge k 3. 2x = ln k