MATH 18 Quiz 6

MATH 18 Quiz 6 (Ch.9) Write your number in the box above. Due: (1) (2) Wednesday, 6-2-2021 Name Let f (x) = 2x − 3 and g(x) = 1 − x2 , find: (a) (f ◦ g)(x) = (1a) (b) (f ◦ g)(−2) = (1b) (c) (g ◦ f )(x) = (1c) (d) (g ◦ f )(−2) = (1d) The function f (x) = 3x − 7 is a one-to-one function, find its inverse function f −1 (x): (show work) (2) (3) An initial deposit of $500 earns 5% annual interest compounded quarterly (k = 4), how much will be in the account after 10 years? Use the formula A = A0 (1 + kr )kt and round answer to the nearest dollar. (Show work.) (3) (4) Assume that $1 were deposited on July 4, 1776 at 5% annual interest interest rate, compounded annually. What would it be worth on July 4 of this year? (4) (5) Use a scientific calculator to find the following power values (rounding off to 4 decimal places): (a) 53.25 = 0.31.6 = (d) (6) (b) 120.34 = (e) 0.88−5.1 = Rewrite the following exponential form into logarithmic form: 1 (7) (a) 25 2 = 5 (6a) (b) ( 23 )−3 = 27 8 (6b) (c) x5y+1 = 3z + 4 (6c) Rewrite the following logarithmic form into exponential form: (a) log7 343 = 3 (b) log125 25 = 2 3 (c) loga (2c + 5) = 3d (8) (9) (c) 100−1.2 = (7a) (7b) (7c) Find the value of x: (a) 22x−1 = 8 (8a) (b) ( 13 )x−6 = 9 (8b) (c) log16 x = 5 4 (8c) (d) logx 5 = 1 (8d) (e) log49 7 = x (8e) Find the following logarithms by the properties of logarithm, (without using a calculator): (a) log25 1 = (b) log3 (c) log2 16 = (9c) (d) log9 9 = (9d) √ 3= (9a) (9b) (e) log10 1000 = (9e) (f) 1 log10 ( 10 )= (9f) (g) log10 4 + log10 25 = (9g) (h) log10 70 − log10 7 = (9h) (i) log2 (−4) = (9i) (10) Expanding the following logarithms: (rewrite each of the following logarithms to a sum of logb x, logb y, and logb z if possible), show work. (a) logb x3 y 5 = (10a) (b) 2 logb yx3 z 4 = (10b) (c) logb q (11) 5 x3 y z 2 w4 = (10c) Condensing the following logarithms: (rewrite each of the following to ONE logarithm) (a) 3 logb x + logb y = (11a) (b) 2 logb x − 3 logb y + 4 logb z = (11b) (c) (12) 1 (3 logb x − 4 logb y) 5 = (11c) Given that logb 2 = A and logb 3 = C, use the properties of logarithm to express the following logarithms in terms of A and C : (a) logb 12 = (b) logb 81 = (c) logb √ 5 2= (d) logb 27 32 = (12a) (12b) (12c) (12d) (13) Find each of the following logarithms, using a scientific calculator and the Change-of-Base formula, (keep 4 decimal place in the answers). (a) (14) (a) log5 10 ≈ (b) log9 0.2 ≈ (c) log0.3 2.5 ≈ Solve the following exponential equations for x, show work: Solve the equation: 3x 2 +2 = 27x (14a) (In (b) and (c) You can leave the logarithms in the answer, or use a calculator to find the approximation of x to the nearest thousandths) (b) 52x−1 = 9 (14b) (c) 3x = 5x+3 (14c) (15) Solve the following logarithmic equations for x, show some work: (a) log4 x + log4 (x − 3) = 1 (15a) (b) log(5 − 4x) = 2 log x (15b) (c) log x + log(3x − 5) = log 12 (15c) (d) log2 (7x + 3) − log2 (2x − 3) = 3 (15d) (16) Determining whether the following statements are True (T) or False (F): (a) log2 (8 + x) = 3 + log2 x (c) logb (d) log5 (100) = 2(1 + log5 2) 3x 5y (b) log2 (8x) = 3 + log2 x = logb 3 + logb x − logb 5 + logb y (e) logb x logb y = logb x − logb y Math18 Quiz 6, 40 points
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