1. Find x if 2log, 5 + -log, 9- log, 3 = log. I 2. Solve log,(x -2) + log, (x +3) = log, 14. 3. Solve logo(x +4) + logo(x -2) = log.(4x) 4. Solve the following exponential functions for x a) 42x-1 = 3x+2 b) 72x-3 = 2-3x 5. Evaluate each of the following logarithms. a) log2 32 b) log3 (7) 16. Suppose you invest $1000 in an account that pays 6% interest, compounded annually. The amount, A, in dollars, in the account after any given time, t, in years, is given by the equation A = 1000(1.06) . Determine how long it takes for your investment to double, and to triple, to the nearest tenth of a year. 7. Use the decibel scale 82 - 81 = 10 log (;) to answer the following a) The sound as a subway train passes is about 315 times as intense as normal city traffic, which has a decibel level of about 85. What is the decibel level of a passing subway train? b) A worker using a power saw hears a decibel level of 118. How many times as intense as the sound of normal city traffic is the sound of a power saw? Loud Rocket 200 Potentially fatal Jet engine 160 Rock concert speaker 150 Pain threshold Symphony (peak) 120 Maximum stereo output 100 Niagara Falls 90 Protective hearing equipment Normal city traffic 8.5 Shout recommended Normal conversation Whisper 30 Barely audible Rustle of leaves 10 Quiet 8. Let / (x) = vx - 9 and g (x) = = Write a simplified algebraic model for the composite functions given below and state their domain and range. a) f(e(x)) b) g(f(x) 29. Kathy has a small business selling apple cider at the farmers' market. She pays $35 per day to rent her space at the market, and each cup of cider costs her $1. She sells the cider for $2.50 per cup and brings enough cider and cups to sell a maximum of 200 cups in a day a) Write an equation to model each of the following for 1 day, as a function of the number, n, of cups of cider sold. i) her total cost, C ii) her revenue, R b) Identify the break-even point and explain what its coordinates mean c) Develop an algebraic model for the profit function, P(n). d) What is the maximum daily profit Kathy can earn? 10. Solve. Identify and reject any extraneous roots. log (k + 2) + log (k - 1) = 1 log (p + 5) - log (p + 1) = 3