# HW1_Soln - Masnari/Escuti/Brickley ECE200 Fall 2008...

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Masnari/Escuti/Brickley ECE200 – Fall 200 8 – Homework 1 Solution Basic Math and Preliminary Concepts You Need to Know Completely Page 1 of 5 Logarithms 1. Calculate the following: [1 pt each] a. log 10 1 ( ) = 0 b. log 10 0 ( ) = !" , or does not exist c. log 10 0.5 ( ) = -0.301 d. log 10 2 ( ) = 0.301 e. log 10 200 ( ) = 2.301 f. ln 200 ( ) = 5.298 g. e ln 200 ( ) = 200 h. ln e 200 ( ) = 200 i. 10 2.2 = 158.489 j. e 2.2 = 9.025 k. 10 log 10 (200) = 200 l. 10log 10 ln(200) ( ) e ! 1 = 2.664 m. log 10 AB ( ) = log 10 A ( ) + log 10 B ( ) n. ln A B ( ) = ln A ( ) ! ln B ( ) o. log 10 A 2 ( ) = 2log 10 A ( ) 2. Sketch (with axis labels) the following (by hand or with software such as MATLAB): [3 pts each] a. W = x 2 b. X = 10 y c. Y = 10log 10 x ( ) (note that this is known as the Decibel (dB) scale, and we will say that Y is the quantity x expressed in dB)

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Masnari/Escuti/Brickley ECE200 – Fall 200 8 – 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 Y versus X on the following linear graph : b. Plot Y (vertical axis) versus X (horizontal axis) on the following semilog graph :