1. Simplify first, then evaluate. Do not use calculator. (5 Marks) a) log: 24 - log, 3 +log, 2 b) log27 3v3 2. Write the following as a single logarithm 4+ 3[log,(x + 1)- log, (1 -x)] (4 marks) 3. For the function y - - log; (2-2x)+4, determine the following ( 6 marks) a. Equation of the asymptote b. y- intercept c. Domain 6, Determine the point of intersection between the graphs f(x) = 3(2)" ' and g(x) = 2(3)". ( 6 d. Range Marks) 4. Given y= -2.(5) +1, determine the following ( 6 marks) Solve for X. Find domain for Logarithm equations. ( 16marks) . Domain: f. Range: g. Equation of the asymptote: by 41+2 + 4% = 136 h. Increasing or decreasing: 5. Sketch the following functions. y = - logal= (x + 1)] + 2 () 1081.5(2x + 3) = 2 State the domain, range, and the intercepts. Give the equation of the asymptote as well. ( 9 marks) dy log(x + 25) - log(x - 1) = 3 B. An earthquake in Japan registered 5.6 on the Richter scale. Another earthquake, in India, was 21 times as intense as the one in Japan. what was the magnitude of the earthquake in India? My-M, = log(;) (4 marks) Thinking ( 4 Marks) 9. If log, a = c and log, b = c, Prove that log, y me-2