CHOATE MA 460 - MA460 Exponential and Logarithmic Functions (2 pages)

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MA460 Exponential and Logarithmic Functions



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MA460 Exponential and Logarithmic Functions

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Pages:
2
School:
Choate Rosemary Hall
Course:
Ma 460 - Honors Precalculus
Honors Precalculus Documents

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MA460 Honors Precalculus Supplementary Problems Exponential and Logarithmic Functions Sketch the graph of each function 1 3 f x 2 x 1 2 x log2 9 2x 2x 2 x 9 4 x 9 log2 2x x If necessary restrict the domain of to make it a one to one function Then find 1 x 5 7 2ln x 1 2ln x 1 x ln x2 16 x ex 2 1 1 6 x 8 x 1 log3 4x 7 Solve each equation for x 9 3x 7 x log 7 3 2 10 log5 x logx 5 11 32x 3x 1 2 0 13 log3 x3 8 log3 x 2 2 x log x 100x 25x 5 32 1 14 log4 2 log4 2 log4 5 16 x x 2 12 6 1 15 log 3 7x 1 log 3 x 2 2 7 16 log x 2 log x 2 17 log x2 log x 2 18 log3 19 e x ln 2 3 4 21 x log3 4 729 3 91 27 4 3 23 3x 3 x 31 2 31 2 3 1 2 log 7 5 25 logx 5 log 7 3 27 2x 2 x 33 2 8 x 1 3 log3 7 21 2 3 20 log 5x 2 75 5 32 22 x log4 2 log4 log4 16 9 243 24 logx 1 0 26 2 52 x 3 7 28 3x 2 34 x 728 Solve each inequality for x 9 29 4 x 3 2 3 31 log3 x 2 2 x 1 30 log2 5 x 2 log2 5 3 32 log1 2 x 1 log1 2 3x 2 e x e x g x ln x 1 2 7 a Find 0 and f ln b Find g x and simplify 5 33 Let f x c Find the domain of the function g 34 Let P0 be the initial population and P t the population at any time t 0 of some mammal in its niche If environmental factors constrain the population growth in such a way that L is the largest population the niche can comfortably accommodate then one model that sometimes describes the population growth or decay is P t L L P0 k L t 1 e P0 where k is a growth or decay factor a If P0 100 L 180 and P 3 160 find k Then sketch the graph b Let y P t Find P 1 y 35 Suppose x a bx 1 8 9 2 and 1 4 3 1 Find a and b 36 Let x 2x 3 1 Find log8 3x 3 1 37 Let x ln sec x 1 ln sec x 1 g x 2 ln tan x Find all x for which x g x Let r log5 2 s log5 3 In terms of r and s find 38 log5 1 5 39 log5 12 40 log5 0 25 41 log5 3 18



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