2. 6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations. Standard: S. Analyze properties and relationships of functions.

3. Logarithms are used to find unknown exponents
in exponential models.
Logarithmic functions define many
measurement scales in the sciences, including the
pH, decibel, and Richter scales.

4. With logarithms, you can write an
exponential equation in an equivalent
logarithmic form.

5. Ex 1.
a. Write in logarithmic form. ________________________
b. Write in exponential form. _______________________
c. Write 112 = 121 in logarithmic form. _________________________
d. Write log 6 36 = 2 in exponential form. _______________________
e. Write 7-2=1/49 in logarithmic form. __________________________
f. Write log 3 1/81= -4 in exponential form. _______________________
2 = log11 121
62 = 36
Log7 (1/49) = -2
3-4 = 1/81

6. You can evaluate logarithms with a base of 10 by using the log key on a calculator.
Ex 2. Solve each equation for x.
Round your answer to the nearest thousandth.
a). 10x= 1/ b).
x = log101/109
x =
c). 10x= d). 10x= 7210
x = log x = log107210
x = x = 3.858

7. The inverse of the exponential function
y = 10x is x = 10y.
To rewrite x = 10y in terms of y,
use the equivalent logarithmic form,
y = log 10 x.

8. Examine the tables & graphs below to see the inverse relationship between y=10x and y = log10x.

9. Range: all positive Real #s
BeBelow summarizes the relationship between the domain and range of y = 10x and of y = log10 X.
y = 10x
Domain: all Real #s
Range: all positive Real #s
y = log10 X
Domain: all positive real #s
Range: all Real #s

10. The logarithmic function y = log b x with
base b, or x = by, is the inverse of the
exponential function y = bx,
where b ≠ 1 and b > 0.
One-to-one Property of Exponents
If bx = by, then x = y.

11. Ex. 3 Find the value of v in each equation.B.
5 = logv 32
v = log125 5
v5 = 32
125v = 5
(53)v = 5
v5 = 25
53v = 51
v = 2
3v = 1
v = 1/3

12. d. v = log464
4v = 64
4v = 43 (same base)
v = 3 c.
4 = log3 v
34 = v
81 = v

13. e. 2 = logv25 v2 = 25 v2=52 v = 5 f. 6 = log3v v = 36 v = 729
g. v = log
10v = 1000
10v = 103
v = 3
e. 2 = logv25
v2 = 25
v2=52
v = 5
h. 2 = log7V
V = 72
V = 49
f. 6 = log3v
v = 36
v = 729
I. 1 = log3v
31 = v
3 = v

18. Homework
Integrated Algebra II- Section 6.3 Level A
Honors Algebra II- Section 6.3 Level B
Read article and write one paragraph on your thoughts as they relate to the exponential growth of money