Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewHere simplify means use Property 1 - 7 from the Logarithm Properties section asoften as you can. You will be done when you can’t use any more of these properties.Property 5 can be extended to products of more than two functions so,ln xyz = ln x+ ln y + ln z3 4 5 3 4 5= 3ln x+ 4ln y+5ln z2.⎛49x⎞log3⎜y ⎟⎝ ⎠SolutionIn using property 6 make sure that the logarithm that you subtract is the one thatcontains the denominator as its argument. Also, note that that I’ll be converting theroot to exponents in the first step since we’ll need that done for a later step.41⎛9x⎞4 2log3 = log39x− log3y⎜y ⎟⎝ ⎠14 23 3x3y= log 9 + log −log1= 2 + 4log3 x−log3y2Evaluate logs where possible as I did in the first term.3.⎛log x +y⎜⎝2 2( x−y)3⎞⎟⎠SolutionThe point to this problem is mostly the correct use of property 7.⎛ 2 2x + y ⎞log = log + −log−3⎜( x y)⎟⎝ − ⎠= log + − −2 2( x y ) ( x y)2 2( x y ) 3log ( x y)You can use Property 7 on the second term because the WHOLE term was raised tothe 3, but in the first logarithm, only the individual terms were squared and not theterm as a whole so the 2’s must stay where they are!3Solving Exponential Equations© 2006 Paul Dawkins 90http://tutorial.math.lamar.edu/terms.aspx