in this presentation you can see te properties and some examples and exercises

1. LOGARITHMS

2. LOGARITHMS
Logarithms are the inverse of exponentials.
Exponential Logarithm
23=8 푙표푔28 = 3
How many 2s do we multiply to get 8?
Logarithm is a power we
need to raise a another
number
 To solve this problems we use a function called logarithmic function.

3. Logarithmic function
y= logb x
b= base (value of the logarithm)
x=output value (number we want to find the value)
y= input value (exponent in the inverse)
푙표푔28 = 3
2= b
8= x
3= y

4. Base: common base 10
Since our calculators only use base
10, this means is going to be a
common logarithm.
Example:
푙표푔10 1000
In calculator
log (1000) = 3

5. Properties of logarithms
Properties let you solve exponential equations without the need of substitute
the base by power of 10.
Product of a logarithm 풍풐품풃푨 + 풍풐품풃푪 = 풍풐품풃 (푨 ∙ 푪)
Example
푙표푔2 8+ 푙표푔232
23 = 8 25 = 32
23 ∙ 25 = 23+5 = 28

6. Quotient logarithm
푙표푔푏퐴 − 푙표푔푏퐶 = 푙표푔푏 (퐴
퐵)
Power logarithm
퐴 ∙ 푙표푔푏퐶 = 푙표푔푏 (퐶 퐴)
푙표푔3
1
9
1
9
− 푙표푔381 = 푙표푔3(
∙
1
81
)
푙표푔3
1
9
1
9
− 푙표푔381 = 푙표푔3(
∙
1
81
1
729
)= 푙표푔3(
)
32 = 9 34 = 81
32+4 = 36
Example
3 ∙ 푙표푔28 = 푙표푔2 (83)
Example
3 ∙ 푙표푔28 = 푙표푔2 83 = 푙표푔2512
3 . 3= 9
29 = 512
2

7. THE PROPERTIE OF CHANGE ONE LOGARITHM OF BASE
DIFFERENT THAN 10
Logb = loga x
loga b

8. If x= log2 45:
2 = 45
Log 2 = 45
x log2 = log 45
X= log 45
Log 2
Log2 45= log 45
Log 2
x
x
SOLUTION:
1. DEFINITION OF LOGARITHM Log 2 45=5.491853…
2.-FIND THE LOGARITHM OF BOTH SIDES
3.- POWER OF A LOGARITHM
4.- DIVIDING BY LOG 2

9. GRAPH A LOGARITHMIC FUNCTION
FOR EXAMPLE: y = log 5 x
X Y= f (x) = log 5 x
1 0.7
2 1
3 1.18
4 1.3
0 error
-1 error

10. QUIZ
1. y=f(x)=log 2x
2. y=f(x)=log ½
3. y=f(x)=log2 2x
4. y=f(x)=log5x
RESOLVE THE
PROBLEMS:
x= log7 56:
x= log4 27:
x= log6 39:
x= log3 72:

11. solve the exponential equations using the
properties of the logarithms
a) Log3 6+ log3 81= log3 486
b) 푙표푔3
1
9
− 푙표푔381 = 푙표푔3(
1
9
∙
1
27
)