Masnari/Escuti/BrickleyECE200 – Fall 2008– Homework 1 Solution Basic Math and Preliminary Concepts You Need to Know Completely Page 1 of 5 Logarithms1.Calculate the following: [1 pt each]a.log101()=0b.log100( )=!", or does not existc.log100.5()=-0.301d.log102()=0.301e.log10200()= 2.301f.ln 200()=5.298g.eln 200()=200h.lne200()=200i.102.2=158.489j.e2.2=9.025k.10log10(200)=200l.10log10ln(200)()e!1=2.664m.log10AB()=log10A()+log10B()n.lnA B()=lnA()!lnB()o.log10A2()=2log10A()2.Sketch (with axis labels) the following (by hand or with software such as MATLAB): [3 pts each]a.W=x2b.X=10yc.Y=10log10x()(note that this is known as the Decibel (dB)scale, and we will say that Yis the quantity xexpressed in dB)
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Masnari/Escuti/BrickleyECE200 – Fall 2008– Homework 1 Solution Basic Math and Preliminary Concepts You Need to Know Completely Page 2 of 5 3.Consider the following data: [5 pts each]X = 1 10 100 1,000 10,000 Y = 12 11 10 2 0.1 a.Plot Yversus Xon the following linear graph: b.Plot Y(vertical axis) versus X(horizontal axis) on the following semilog graph: