13: Math 112 Written Homework: Properties of Logarithms Student Name:____________________________________________ Instructor: J.M.S. Liston Math 112 Section:________ Directions: ANSWER THE FOLLOWING QUESTIONS ON YOUR OWN BLANK, WHITE PAPER (e.g. printer paper). Begin by first stating what you know, then what you're trying to find; be sure to SHOW ALL WORK to reflect your thinking and calculations. Explanations should be given in complete sentence (i.e., subject and verb). If you solve with a graph, it should be drawn accurately, SCALED, both axes identified with units. Staple this page to the TOP of your work. Be sure to put your name on all submitted pages. Failure to follow these instructions will result in a lower grade. 1. Use properties of logarithms to completely expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions. log ( 20 x1 y ) 2. Use properties of logarithms to rewrite as a single logarithm: 1 7 log 5 ( x )3 log 5 ( y ) log 5 ( z )+11 log 5 ( w) 9 3. Use properties of logarithms to rewrite as a single logarithm: 3 log ( x )+ 6 log( y) 4. Use properties of logarithms to completely expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions. log 2 ( 16 a2 b c d ) 1. $4,000 is invested in an account bearing 8% interest compounded continuously. The amount of time it takes for the money to grow by a factor of x is given by t=f ( x)=8 ln (x) . (For example, the amount of time required for the investment to double is f (2)=8 ln (2) . How long will it take the balance in the account to 1 reach $6,000? Find a formula for the inverse function. Evaluate f ( 8) and explain what this tells you in practical terms