Notesale: Turn your study into money

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Module: BIOM – 1007

Lecturer: Dr Weldon

Date: 14/11/16

Logs
o

A logarithm is a quantity representing the power to which a fixed number (the base) must be raised to
produce a given number
 The common base is 10 but any number can be used as the base
 The common base is written as log(x)
 E
...
log (100) = 2
 Any other number is written as logn(x)
 E
...
log2(8) = 3

o

A logarithmic graph is the opposite of an exponential graph (see right)
 They both are asymptotes; the logarithmic graph is to the y axis
whereas the exponential graph is to the x axis

o

All numbers lower than one have negative logarithms
 E
...
log(0
...
g
...
g
...
699

o

Logs are used in scientific applications to compare numbers of great various magnitude
 For example, time scales vary from billions of years to fractions of seconds
 Here is an example of times that can be compared:
 Formation of earth – 4
...
5x107 YBP
 Last great ice age – 1x104 YBP
 Declaration of independence – 2x102 YBP:
 And here they are as their logs (YBP)
 Formation of earth – 9
...
813
 Last great ice age – 4
...
301
 Note the difference in the ability to see the graphs:

Logs (YBP)

Years Before Present

Series 1

Series 1
5E+09
4E+09
3E+09
2E+09
1E+09
0

12
10
8
6
4
2
0

o

The reverse of taking a log is called the antilogarithm
 This is obtained when you raise 10 to that number
 E
...
log-1(2) = 100
 E
...
log-1(-4) = 0
...
71828)
 This is written as ln(x)

o

The common log can be used to measure pH (potential of hydrogen)

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