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)

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
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
: