Content Page Common Logarithm Introduction History Henry Briggs Calculators Change of Base Law Graph Natural Logarithm Introduction History Graph

Common Logarithm - Introduction Common Logarithms are logarithms to base 10 Commonly abbreviated as lg Hence, for example

Common Logarithm - History Sometimes called Briggsian Logarithm Named after Henry Briggs, a 17 th century mathematician In calculators, when you press log It is actually log 10 or lg This is because base 10 logarithms are useful for computations Engineers often used log to represent log 10 Since engineers programmed calculators, log became log 10

Common Logarithm - History However, this is extremely misleading So we have to take note in case we make such a mistake by confusing log 10 with log We often need to make use of logarithms of non-10 bases Hence, we will briefly cover the Change of Base Law

Common Logarithm – Change of Base Law If 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 Law This law can be used to convert common logarithms to natural logarithms, and vice versa log 10 N = log e N / log e 10 = (ln N) / (ln 10) = (ln N) / = × ln N

Natural Logarithms- Introduction Beside base 10, another important base is e where e= (5 d.p) Logarithms to base e are called natural logarithms “log e” is often abbreviated as “ln”

Natural Logarithms- Introduction Natural logarithms may also be evaluated using the “ln” button on a scientific calculator. By definition, ln Y = X Y = e x

Natural Logarithms- History A mathematics teacher, John Speidell, compiled a table on the natural logarithm in The first mention of the natural logarithm was by Nicholas Mercator in his work Logarithmotechnia published year It was formerly known as the hyperbolic logarithm.

Natural Logarithms- Examples 1. ln p = 3 2. log e p = 3 3. p = e³ 1. e 2x = k 2. 2 x = log e k 3. 2 x = ln k