Natural Log - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 5.1A ‘“.&=* LT: Graph natural log & use wauutennimtees Notes \ine= | e Parent graph... © Vertical asymptote: x = 0 (graph goes to -~) o x-intercept: (1,0) ® Equation: y= aln(x—h) +k o his horizontal shift o kis vertical shift o ais vertical stretch = Bigger than 1: taller = Smaller than 1: shorter = Negative: reflect in x-axis LT: Rearrange expressions using log properties Notes e Natural log properties... a Domain: (0, ©) — no negative arguments Y= ‘nk o Inl=0 o Inab = tee atin a ° In5 =Ina—Inb o Ina” =4rret nln aw Examples Use log properties to expand the expression. 1) 7% ) ae (\n Ky — \n4 In xeIny - Int Ye AS 2) x +2 ee (x42) — In 2} Use log properties to write the expression as a log of a single quantity. 3) @[Inx + In@ — 2) ln@es3)] 1/2