Questions 1 till 6 with steps please

Practise For help with questions 1 and 2, refer to Example 1. 1. Evaluate. For help with questions 5 and 6, refer to Example 3. a) log, 163 b) log, 82 5. Evaluate, correct to three decimal places. c) log 100-4 d) log 0.12 a) log, 23 2. Evaluate. b) log, 20 a) log, V8 c) log, 2 b) log, V243 () log, (V81)6 d) -log, 4 d) log. (16) 15 e) log1 30 For help with questions 3 and 4, refer to Example 2. f) log3 (8) 3. Solve for t to two decimal places. 6. Write as a single logarithm. a) 10 = 4' b ) 5' = 250 log 8 log 17 () 2 = 1.08 b ) d) 500 = 100(1.06)' log 5 log 9 4. An investment earns 7% interest, compounded log log( x + 1) annually. The amount, A, that the investment log(x - 1) is worth as a function of time, t, in years, log is given by A(t) = 500(1.07). a) Use the equation to determine the value of For help with questions 7 and 8, refer to Example 4. the investment 7. a) Sketch a graph of the function f(x) = log, x by first graphing the inverse function i) initially, when t = 0 f'(x) = 2* and then reflecting the graph ii) after 2 years in the line y = x. iii) after 4 years b) Use Technology Check your graph using b) How long will it take for the investment to graphing technology. i) double in value? 8. Use Technology Use graphing software or a graphing calculator to graph f(x) = log, x. ii) triple in value? 9. Solve for x, correct to three decimal places. CONNECTIONS a) 2 = log 3x