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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