1. Precalculus Section 5.5 Define and apply logarithms
Use logarithms. y = log2x (read as y equals the base 2 log of x)
y = log2x is the inverse of y = 2x.
A logarithmic function is the inverse of an exponential function.
Recall the equation of an exponential function.
y = 2x
What is its inverse?
x = 2y
How do you solve for y?
Definition: logbx = a if ba = x.
Note: b>0,≠1, and x>0
read as the base b log of x equals a.

2. The graphs of the exponential function y = 2x and its inverse y = log2x are symmetrical about the line y=x

3. Write the following in exponential form using the definition: logbx = a if ba = x.
example log416 = 2 log464 = 3 log6(1/36) = -2
solution 42 = = = 1/36

4. Simplify the expression
example log39 log3243 log4
Solution

5. Special logarithms Common logarithms have a base of 10.
log x = a means log10 x = a and 10a = x
Examples log 100 log 1/100 log 10,000 log 1

6. Natural logarithms have a base of e
ln x = k means loge x= k and ek = x
example ln e2 ln (1/e) ln √e

7. More examples: note…if the base of a logarithm is the same as the base of an exponential function they “undo” each other.
Example solution

8. Solve the logarithmic equation
log4x = 1.5
ln (ln x) = 1

9. Solve the logarithmic equation
log 18.3 = x log .56 = x ln 72 = x
log x = 2.15 log x = -2.5 ln x = 5.6

10. solve
ex = x = 473

11. The loudness of a sound is measured in decibels
The loudness of a sound is measured in decibels. The formula to calculate decibels involves logarithms.
Decibel level = 10 log
I = intensity of the sound
Io = intensity of the threshold of hearing
Find the decibel level of a sound that has an intensity of 100 Io.

12. Find the decibel level of two sound sources if each has an intensity of 100 Io.

13. Assignment
Page 195
Problems 2-18 even, 24,25,26,36-46 even