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UNIT
4 : EXPONENTIAL & LOGARITHMIC
FUNCTIONS
LESSON 6: LOGARITHMIC & EXPONENTIAL
EQUATIONS II
The following properties
of logarithms are important and used frequently in our study of
logarithms.
They correspond closely to
our rules for exponents studied earlier.
Note: When we
read log_{2}8, we ask the
question To what exponent must base 2
be raised to give 8? The answer is of
course 3
and this idea gives rise to the
following definition.
Definition:
the expression log_{a}x is defined to mean the exponent to which base a must
be raised to give x.
The expression reads:
the logarithm of x, base a.
Hence log_{10}100 means the exponent to which
base 10 must be raised to give 100. The
answer is 2, giving the statement log_{10}100
= 2.
Hence log_{3}81 means the exponent to
which base 3 must be raised to give 81.
The answer is 4, giving the statement
log_{3}81 = 4.
Note: See # 12 in homework questions for more
examples