22. Given that log3 a = 6 and log3 b = 5, determine the value of log3 (27ab2). 23. An earthquake measuring 5.3 on the Richter scale is 125 times more intense than a second earthquake. Determine to the nearest tenth, the Richter scale measure of the second earthquake. 24. The population of a city was 173500 on January 1, 1998, and it was 294000 on January 1, 2012. If the growth rate of the city can be modeled as an exponential function, then the average annual growth rate of the city, expressed to the nearest tenth of a percentage, was 25. The logarithmic function y = log1 x has undergone a horizontal stretch about the y - axis by a factor of 16. This can be expressed in the form: y = logix + b. Determine the value of b. 26. The population of a town is decreasing exponentially by 30% every 5 years. If the current population is 9355, what will the population be in 18 years?15. Determine the domain of the graph of y = logb (-3 x + 12 ), where 0 - 9 b ) x 9 d) x 2 b) log ( x 2 - x - 2), - 2 2 d) 7 log ( x -4) x > 2 log ( x-2 ) ' 10. (log 2x)2is equivalent to: a) 2 log(2x) b) log(4x2) c) 2log (4x) d) (log 2)2 + 2 log(2) log(x) + (logx)2 11. The equation : m logp n = q can be written in exponential form as: a) p9 = mn b) n9 = pm c) pm = n d) p = mnSHOW YOUR WORK FOR FULL MARKS FOR ALL PROBLEMS 1. When 16(8)2(*-2) is converted to base 2, the exponent will be: a ) NIW b) ; x-2 C) 7x - 14 d) 6x - 12 2. What is the y value of the y-intercept of: y = 3bx-2, b > 1 a) b) -362 C ) d) 3 3. The equation y = log2 x2 can also be written as: a) y = 2z b) x = 22 C) 22* = y d) 22y = x 4. The equation of y = b*, x > 1, if x is replaced by 2x and y is replaced by (y + 4) which of the following statements describe the transformation? a) The point (x, y) on f(x) has been transformed to the point (2x, y - 4) b) The point (x, y) on f (x) has been transformed to the point ( , y - 4) c) The point (x, y) on f (x) has been transformed to the point (2x, y + 4) d) The point (x, y) on f (x) has been transformed to the point (, y + 4) A student is attempting to graph f (x) = x - m - n, what is the equation of the asymptote of f (x)? a ) y = m b) y = -m c) x = -n d) y = -n