(1) Find the following; (@) logy(16) (b) log(1) (c) log,(243) (Hint: remember you are looking for a power.) (2) Convert into exponential form: log,(a) = b (Hint: in other words give the same information without mentioning logs.) (3) Evaluate the following: (a) log, (}%) (b) log;(v'T) (c) log(0.01) (d) In(e) (4) Answer these questions about the function log;(x) (a) Sketch its graph. Include at least two points on the graph and draw the vertical asymptote. Remember to number and label the axes. (b) Give its domain. () Give its range. (d) Where is it positive? Give your answer in interval notation. (5 Sketch the graph of log,(x 2) 1 by transforming your graph from the last question. Make sure to show the new vertical asymptote and new = intercept. 6 v Expand as much as possible and simplify: log, (_J;: ) 7 v If log,(x) =18 and log,(y) = 2 then find: (@) log,(zy) (b) logy(x/y) () log,(y") (d) log,(b) (Hint: Use the properties of logs such as the product and quotient rules. Can you see why the answer to (a) is 20?) (8) Combine into a single logarithm and evaluate: log(6) + log(50) log(3) (9) Use the change of base formula to express log,(30) using the natural logarithm (with base ). Then use your calculator to evaluate it correct to 4 decimal places. Since 3 = 27 your answer should be a bit bigger than 3. (10) Solve the exponential equation 2* = 10 and give the solution in terms of logs and as a decimal. (Do you see why = must be between 3 and 47) (11) Solve the exponential equation: 4 - 2%+ = 16*+* (12) Solve the logarithmic equation: 5 + log,(3z 1) =8