Logarithmic Functions
Objective: You will be able to write
the equivalent form of a logarithmic
or exponential function as an
exponent or logarithm.
The logarithmi c funtion to the base b,
where a  0 and a  0, is denoted by
log b x  y and is definded by :
log b x  y if and only if b  x
y
logarithmic form
exponential form
log b x  y  b  x
y
base
exponent
base exponent
• b is positive with b  1
Logarithmic
inverse form
exponential form
log b y  x  b  y
x
base
exponent
base exponent
• b is positive with b  1
Logarithm and Exponential
Function Equivalent Forms
The equivalent of
y  b is the function
x
log b y  x
x
What if you knew 8192  2 . How would
you find x?
Use the definition of a logarithm: x  log b y
And with the little help of a calculator we
find log 2 8192  x is x  13 .
Exponential
Logarithmic
1.
2.
3.
4.
4  64
log 4 64  3
x y
log x y  z
3
z
Exponential
Logarithmic
1. log 2 32  5
2  32
2.
log 3 7  y
3 7
3. log 3 a  7
3 a
4. log 3 9  2
5.
6.
5
y
7
3 9
2
1
7
2
7  7
1
log 3  4
81
1
3 
81
log 7
1
2
4
The Common Logarithmic Function
base =10
y  log 10 x 
x  10
y  log x  x  10
y
y