Revised 2018 11. Simplify each log expression: ogM 3logN 2l0g b 2logc-logD logE

Question

Revised 2018 11. Simplify each log expression: ogM 3logN 2l0g b 2logc-logD logE a. 12. Write a log expression to represent the value of x: a. 3* 25 b. 3x+1-25 ?. 3-"-25 13. Which of the following is NOT equivalent to the equation 7 12 10g 7* log 12 log 12 log 7 log12 7-x x log 7-log 12 A. C. B. D. 14. Identify each of the following sequences as arithmetic, geometric or neither. a. 1, 4, 9, 16, 25,. For problems 15-16, choose from the following formulas b. -7, 4,-1,2, 5, c 9,-3,1, 39 1-r 1-r 15. Given the sequence: 12, 18, 24, 30, . 204, find the following: a. the total number of termsb. the 25 d. the explicit formula term C.the sum of the first 25 terms e. the recursive formula f.given , -528, findn 16. Given the sequence: 5, 15, 45,135,find the following: b. the sum of the first 8 terms a. the 12 term c. the explicit formula d. the recursive formula e.given ,-7,971,615, find n 17. Graph each of the following functions and identify the requested information: a. y (x1)0x-5)0x+3) b. y (x+ 2)(x -1) CY (-1)0x + 2)x-3)x +4) relative maxima: relative minima: zeros: d. y (x+ 2)'(x -3) ym(3-x)(x + 2)(x-1) domain: e, range: 18. Find the roots of each equation: a. 3x + 17x+18x-8- b. xx+10- cx +4x+ 2x-4-0 P(x) 19. Given the graph at the right, determine the following information: a. the roots b. the factors c. the equation in factored form d. the equation in expanded form

Explanation / Answer

11) a ) log M + 3 log N + 2 log P

= log ( M * N^3 * P^2 )

= log ( MN^3P^2 )

b) 2 log C - log D + log E

= log ( C^2 E / D )

c) 5 ( log A - log B )

5 log ( A/ B )

log ( A/B )^5

2) a ) 3^x = 25

taking log on both sides

x log 3 = log 25

x = log 25 / log 3

b) 3^(x+1) = 25

x+1 log 3 = log 25

x = ( log 25 / log 3) -1

c) 3^-x = 25

- x log 3 = log 25

x = - log 25 / log 3

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