Definition: Common Logarithms are Powers or Exponents of Ten
Examples: … 10-3 10-2 10-1 100 10+1 10+2 10+3 …
Values: … .001 .01 .1 1 10 100 1000 …
The study of common logarithms
is beneficial in the evaluation of Exponential and
Logarithmic expressions as well
as the solution of Exponential and Logarithmic
Equations. Many times in Advanced Mathematics such
expressions and equations
do
arise and students need understand and to be able to compute these topics.
Exponential & Logarithmic Formulas
Log
of a Number = Exponent. Antilog of an
Exponent = Number.
LogB
N = E BE = N AntiB E = N
Log10 100 = 2 102 = 100 Anti10
2 = 100
Common Logarithms are relative
easy to understand and to compute when they are
Integer Values: … -3, -2,
-1, 0, +1, +2, +3, … However,
many times they are not.
Using a Scientific Calculator
makes the evaluation of non-interger exponents rather
easy
but only if a student really understand the above definitions and examples.
A Free
and Online Scientific Calculator and Plotter is
available: GraphCalc
A Free
and Online Table of Common Logarithmic Values: Common Log Table
It is useful for understanding
the process of evaluation of non-integer exponents
to
be able to complete the following interpolation process used in the good ole
days.
Interpolation (Estimation) Process
Determine
the Value of X for .006! Estimate
of X is ????… Why?
10-3 10x 10-2 -3 X -2
.001 .006 .01 .001 .006 .010
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The Graph of 10X
in Black asymptotic to X axis and moving upward. Note: Y
Intercept = 0
The
Graph of Log10X in Purple and
asymptotic to Y axis and moving to the right.
Note: X Intercept = 0
Asymptotic - Activity of a line approaching, but never reaching, a given
value. (Asymptote)
Images from Free OnLine Graphing Calculator (GraphCalc) http://www.graphcalc.com
