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
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