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4B: Graphing Logarithmic Functions
Logarithmic Functions
Logarithmic Functions Logarithmic Functions
Logarithmic Functions –
––
–
The Inverse of an Exponential Function
The Inverse of an Exponential FunctionThe Inverse of an Exponential Function
The Inverse of an Exponential Function
The inverse of an exponential function ݂ሺݔሻ= ܾ
௫
is called the logarithmic function with base
logarithmic function with base logarithmic function with base
logarithmic function with base ࢈,
which we write as log
ሺݔሻ or log
ݔ. Written as inverses, we say if ܾ > 0 and ܾ ≠ 1
if ݂ሺݔሻ= ܾ
௫
, then ݂
ିଵ
ሺݔሻ= log
ݔ
Remember: Converting between Logarithmic and Exponential form:
If ݔ > 0 and 0 < ܾ ≠ 1, then ݕ = log
ሺݔሻ is equivalent to ܾ
௬
= ݔ.
That is… ࢀࢎࢋ ࢍ ࢙ ࢚ࢎࢋ ࢝ࢋ࢘!
Try these:
Write each logarithmic equation in exponential form to solve for the variable.
aሻ log
ଶ
ሺ8ሻ= ݕ
bሻ log
ଶ
ቀ
ଵ
଼
ቁ = ݕ
cሻ log
ହ
ሺ25ሻ = ݕ
dሻ log
ଷ
ቀ
ଵ
ଽ
ቁ = ݕ
Consider This:
Consider This:Consider This:
Consider This:
Can you find the logarithm of a non-positive number? That is, could you find the
following logarithms: log
ଶ
ሺ0ሻ =? , log
ଶ
ሺ−8ሻ =?
Explain why or why not.
Graphing Logarithmic Functions
Graphing Logarithmic FunctionsGraphing Logarithmic Functions
Graphing Logarithmic Functions
Complete the tables and use them graph the functions by hand on the same graph.
ݕ = log
ଶ
ݔ ݕ = log
ଷ
ݔ
ݔ
ݕ
16
8
4
2
1
1
2
1
4
1
8
ݔ
ݕ
9
3
1
1
3
1
9
