LOGARITHMS
Algebra
Example 6:
Calculate log10 1.
Solution:
Rule 6.
logb 1 = 0
log10 1 = 0
Example 7:
Calculate -log10 2.
Solution:
Rule 7:
logb (1/A) = -logbA
-log10 2
= log10 (1/2)
= -log10 0.5
= -0.3010
Common and Natural Logarithms
In scientific and engineering practice, the natural system of logarithms uses the number
2.718281828459042. Since this number is frequently encountered, the letter e is used. Many
natural occurrences can be expressed by exponential equations with e as the base. For example,
the decay of radioactive isotopes can be expressed as a natural logarithm equation. These
logarithmic expressions are called natural logs because e is the basis for many laws of nature.
The expression ln is used to represent a logarithm when e is the base. Therefore, the exponential
equation is written as
ex = N.
and the logarithm expression is written as
loge N = x
or
lnN = x.
As with base 10 logs (common logs), natural logs can be determined easily with the aid of a
calculator.
MA-02
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