Tutoring Worksheet for Basic Logarithms 1. Evaluate the following ...

Tutoring Worksheet for Basic Logarithms1. Evaluate the following logarithmic expressions:⎛ 1 ⎞log 64 b. log3⎜ 27⎟⎝ ⎠a.8c.log510 d.⎛1⎞ln⎜e⎟⎝ ⎠2. Expand the following logarithmic expressions completely so that it is in a form where there isnot a logarithm of a product, quotient, or power:a. log3( x y )b.⎛log⎜xy3⎝ z2 4⎞⎟⎠c.log2⎛xx⎜⎝ x2( + 1)2− 1⎞⎟⎠3. Rewrite as a single logarithm:3a. log46 + 3log42b. log5( x −1) − 2log53c.7+7−72(log x 2log y 3log z)4. Solve the following equations using logarithms:3a. 2 x x= 34b. 4(1 10 ) 1 11+ − = c. 2log (2 − x) = 3kt5. Application: Using Newton’s Law of Cooling, Tt () = Ts+ De −0, where D0is the initial temperaturedifference between an object and its surroundings, the surroundings temperature is Ts, t is the timethe temperature is taken, and k is a positive constant depending on the type of object, solve thefollowing:A cup of coffee has a temperature of 200 o F and is placed in a room that has a temperature of 70 FAfter 10 minutes, the temperature of coffee is 150 Fo .A. Find a formula for the temperature of the coffee at time t.B. Find the temperature of the coffee after 15 minutes.C. When will the coffee have cooled to 100 o F ?o .

Answers – Tutoring Worksheet for Basic Logarithms1. a) 2 b) –3 c) 5 d) –12. a) log3 x log31+ y b) 2log x + 4logy − 3log z21log + log ( + 1) − log ( − 1)22 2c)2x2x2x3. a)43log 48 b) log (8( x − 1))5c)log⎛⎜xy ⎝ z7 322⎞⎟⎠4. a) x ≈ 1.7b) x ≈ 0.3 c) x = − 60.048555. a) Tt ( ) = 70 + 130e −t0.04855(15)b) −oT(15) = 70 + 130e ≈133Fc) t ≈ 30.2