16) Solve the given logarithmic equation for x: log; x +log; (x -6) =3 a) x = 9 or x =-3 b) x =-3 c) x -9 dj no real solution 17) Solve the given logarithmic equation for x: 3In(x -7) +5 =17 a) x = 11 b) x * 32.5 C) X * 61.60 dj no real solution 18) Solve the given logarithmic equation for x: log2 (x -3) =logz x +3 a) x =- b) x = c) x =4 dj no real solution 19) Write a power function y = axb whose graph passes through the points (1. 4) and (4. 8). al y = 4x0.25 b) y = 4x05 c) y = 1/x2 dj y = 2x1/3 20) The graph of the exponential function f(x) = ab* passes through the points (0, 8) and (2. 2). What is the value of f(5)? b) 1/% c) 2 dj 5 21) Which family of functions does this table model? 48 31 0 3 3 22) Which family of functions does this table model? -3 -2 -1 0 512 2 128 3 32 8 2 .5 125 .03125Find the unknown side length. Write your answer in simplified radical form. 1) 2) 2) 3) You have a garden that is in the shape of the right triangle shown. Find the perimeter and area of the garden. 137 in rin Perimeter) Area) Using "special right triangles," find the value of each variable. Leave answers in simplest radical form. 4) 51/2 5) 6) 7) 712 6v/3 30 X = XE X = X = y = y =Find sin R, cos R, and tan R in the triangle. Write each answer as a reduced fraction and a decimal. sin R = 26 20 COS R = 15 tan R = Using a trigonometric ratio, find the value of each variable to the nearest tenth. 9) 10) 17 37 59" X = d= 11) The shadow of a lighthouse is 19 feet long and the angle of elevation is 75. Find the height of the lighthouse. Round your answer to the nearest tenth. -75' h = Approximate the measure of angle A to the nearest degree. 12a) 12b) 29 A 37 C m -3; (-3, x) R: y >-5 : (-5, oc) c) D: x > -5 : (-5, of) d) D: x > -3 ; (-3, xx) R: all real #s ; (-ac, -5 : (-5, ) 2) Identify the equation that would be used to solve the given problem: Suppose you deposit $2000 in a bank account. Find the balance after 5 years if the bank account pays 2.5% annual interest compounded monthly. a) A = 2000(14 2.5 125 b) A =2000 14 .025 15)-025 5 12 12 CJ A =2000( 1+ .025 )125 d) A = 2000e-025s 12 3) Identify the domain and range of the function: f (x) =log2 (x-3) a) D: all real #s ; (-cc, oc) b) D: x > 3 : (-3, ) R: y > -1 ; (-1, ) R: y > -1 : (-1, ) C) D: x > 3 ; (3, c) d) D: x >-3 ; (-3, or) R: all real #s ; (-c, ac) R: all real #s ; (-oc, or) 4) Evaluate the expression: log? a) 2 b) 1/2 C) -2 d) - 1/2 5) Identify the transformations that took place to take the parent function f (x) =log x and transform it into the function g (x) =2log (x+3)-4. (RST)6) Find the inverse of the function: f (x) =log(3x -1) log (3x - 1) b) f -1 (x) =3-10' +1 c) f-1 (x) =log d) f-1 (x) = _10% +1 a) f- (x) = 3 7) Graph: y =log, (x + 2) +3 Asymptote: Domain: Range: 8) Graph: y = 3(2)*-- 4 Asymptote: Domain: Range:9) Condense: log x-log y +log z al log b) log- cJ log x Ulog z d) log (x-y+z) log y 10) Condense: 3log x +log 3 a) log (9x) b) 4log (3x) c) log(3x3) dj log (x] +3) 11) Which of the following statements are not correct? a) log, 48 -log, 16+log, 3 b) log, 48 - 3log, 2+log, 6 c) log, 48 = 2log, 4+log, 3 d) log, 48 =log, 8+2log, 3 12) Which of the following statements is equivalent to log 9+ 3log 2-log 3? a) log 8 b) log 14 c) log 18 d) log 24 13) Solve the given exponential equation for x: 31-1 = 92x47 a) x - 4 b) x- -5 c) x - 5 dj x - -3 14) Solve the given logarithmic equation for x: log, (2x -1) +6 =8 a) x = 32,765.5 b) x = 8.5 c) x = 32 dj x = 40.5 15) Solve the given exponential equation for x: 7 + 42x-5 =71 a x =4 b) x =-3 c) x = 10.5 d) x =-4.5