Question 1-14

Knowledge & Understanding: 1. Evaluate the following expressions: (a) 10g8 2 (b) log1 3 - log:12 (c) 10lost 7+108go 5 (d) log, 1, b >0 Mark Value: 3 2. Convert the following exponential equation to logarithmic form: 47 = 64 (e) log, 64 = x (f) logx 4 = 64 (g) log4 x = 64 (h) log, 64 = 4 Mark Value: 3 3. What type of asymptote is present in a logarithmic function? (e) No asymptote (f) Vertical asymptote (g) Horizontal asymptote (h) Oblique asymptote Mark Value: 3 4. Express as a single logarithm and simplify: 3 log,(a + b) + 2log,(a+ b) -;logic, a+b> 0,c>o Mark Value: 3 Thinking: 5. If loga x = 16, determine the value of log. Vx. (e) 4 (f) 8 (g) 16 (h) 32 Mark Value: 2 6. Jordan is a cryptographer who has been trying to solve the following code: NWP BDLTB. He was given the key for the code, but he has trouble working with logarithms. Given the key below, what is the code? Key: Take the value of x" in the equation logy (logs(log; x)) = 0 and shift each letter in the code that many places back in the alphabet. Mark Value: 3 7. Consider the logarithmic function f(x) = -2log (2(x - 4)). (a) State the x-intercepts, y-intercepts, and asymptotes (if applicable) in this function (b) Sketch a graph of f (x) including the above information. (c) Determine the values of x for which f(x) 2 0. Mark Value: 3 Communication: 8. For what values of x is the logarithmic expression log, (x + 3) + logz x undefined? (e) 350 (1) x5 -3 (g)x50, x= -3 (h) -3 0) (b) D: (x E R x > 2) (c) D:(x E Rlx > -2} (d) DixERx>- Mark Value: 4 13. Solve the following logarithmic and exponential equations for x: (a) 61 =36 (b) log, 4x + log, 5 - log, 2 = 4 (c) 8= (5)3-x (d) loga (x - 2) + 1083x = 1 (e) 64*-2 = 8" V8 Mark Value: 4 14. Explain why log, x"- +1 = m, x > 0. Mark Value: 4