1. Logarithms
ISP 121

2. What is a Logarithm?
A logarithm (or log) is a number that represents a power or exponent
Why use logs?
A simpler way to express large values
Some things grow or shrink exponentially, so the log is a perfect “numbering” system

3. What is a Logarithm? Logarithms are exponents in disguise.
The output of a logarithm is an exponent
log b X = Y ↔ bY = X
The first equation is in “log form” and the second equation is in “exponent form”

4. Converting and Solving
log3 27 = y
3y = 27
y = 3
So log3 27 = 3
log7 49 = y
7y = 49
y = 2
So log7 49 = 2
log525 = y
5y = 25
Y = 2
log525 = 2
log5125 = y
5y = 125
Y = 3
log5125 = 3

5. Log Base 10
The log base 10 (written log10 or just log) is a very common log
log10 x is the power to which 10 must be raised to obtain x
Or better yet, 10 to what power equals x?

6. Log Base 10
Solve the following without a calculator:
log = y
10y = 100
102 = 100
log = 2
Log = y
10y = 1000
103 = 1000
log = 3
log10 10,000 = y
104 = 10,000
log10 10,000 = 4
Log10 10,000,000 = y
107 = 10,000,000
log10 10,000,000 = 7

7. Log Base 10 Review the answers.
Solve the following with a calculator:
Review the answers.
With log base 10, how do the answers change when x is multiplied by 10?
y increases by 1
For log base 10, when y increases by 1, x is multiplied by 10
log10 3 = y
log10 3 = .4771
Log10 30 = y
log10 30 =
Log = y
log =

8. Log Base 10 log 2.5 = y Log 2.5 = .39794 So what is log 25? Log 250?
Use what we learned in the last slide. Remember, log = log10
log 2.5 = y
Log 2.5 =
So what is log 25?
Log 250?
Log 25000?
log 25 =
log 250 =
log 2500 =
Log x = 1
101 = 10
X = 10
So what is x if log x = 2?
what is x if log x = 3?
what is x if log x = 4?
what is x if log x = 6?
log x = 2 x = 100
log x = 3 x = 1000
log x = 6 x = 100,000