Escuti/Masnari 2007
ECE200 – Fall 2007 – Homework 1
Basic Math and Preliminary Concepts You Need to Know Completely
Page 1 of 5
Logarithms
1.
Calculate the following:
a.
log
10
1
( )
b.
log
10
0
( )
c.
log
10
0.5
( )
d.
log
10
2
( )
e.
log
10
200
( )
f.
ln 200
( )
g.
e
ln 200
(
)
h.
ln
e
200
( )
i.
10
2.2
j.
e
2.2
k.
10
log
10
(200)
l.
10log
10
ln(200)
( )
e
!
1
m.
Express
log
10
AB
( )
as the sum of two logarithms (of
A
and
B
)
n.
Express
ln
A B
( )
as the difference of two logarithms
o.
Express
log
10
A
2
( )
in terms of
A
(without the term
A
2
)
2.
Sketch (with axis labels) the following (by hand or with software such as MATLAB):
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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ECE200 – Fall 2007 – Homework 1
Basic Math and Preliminary Concepts You Need to Know Completely
Page 2 of 5
3.
Consider the following data:
X
=
1
10
100
1,000
10,000
Y
=
12
11
10
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 Fall '07
 Escuti
 Basic Math, SEPTA Regional Rail, Logarithmic scale, Natural logarithm, Logarithm, Preliminary Concepts

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