Logarithms
Properties of Logarithms:
• log 1 = 0 = 1
• log = 1 = • log = 1 = 1
• = • = = (One to One Property)
•
If no base is present, it is understood to be base 10 when dealing
with log .
NOTE: When solving logarithm equations, if both sides have the same
base, set the last terms equal to each other (One-to-one property)
Example:log − 6 = log 10
− 6 = 10
= 4, −4
Graphing Logarithms
ALL logarithm graphs follow the same rules that were used to complete
transformations.
Regardless of the base, all log x
graphs are the same
Shifts:
Reflections:
Vertical shift c units up:
ℎ = + Reflect over the x-axis: ℎ = −
Reflect over the y-axis:ℎ = −
Vertical shift c units down:
ℎ = − Horizontal shift c units to the right:
ℎ = − Horizontal shift c units to the left:
ℎ = + Tips:
• To find domain: Set inside of parenthesis > 0
• To find vertical asymptote: Set inside of parenthesis = 0