Download Logarithmic Functions: Definition

Logarithmic function - definition
• The logarithmic function is given by
where:
x0
and
y  log b x
b  0, b  1
y
b x
• Example 1: The function y  log 3 x is a logarithmic
function with base 3, and is equivalent to 3y  x . To
remember this pattern, just think of moving the base 3
under the “y” and remove the “log.”
• Example 2: The function y  log 10 x is a logarithmic
y
function with base 10, and is equivalent to 10  x.
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Logarithmic function - definition
• Example 3: The equation y  log 5 x does not
represent a logarithmic function, since b = -5 < 0.
• The evaluation of a logarithmic expression follows
the pattern of the definition. To evaluate log b c think
of the equation y  log b c , which has the alternate
form b y  c . Finding the value of y translates into
asking the question ...
“b raised to what power yields c?”
• Example 4: Evaluate the expression log 2 8
Since 2 raised to the 3 power is 8, the answer is 3.
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Logarithmic function - definition
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• Example 5: Evaluate the expression log 5
125
1
1
3
Since 5  3 
the answer is - 3.
5 125
• Example 6: Evaluate the following expressions:
Expression
Work
Answer
log b b  ?
log b 1  ?
b1  b
0
b 1
1
log b b  ?
bx  bx
x
x
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Logarithmic function - definition
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