Logarithms and Exponentials: The Great Test
Try these 15 multiple-choice questions ...
Q1.
What means 'ln' ?
(a)
Last Night
(b)
Largely Normal
(c)
Logaritmus Naturalis, the 'natural' logarithm
Check one of
(a)
to
(c)
.
Q2.
OK, something more difficult for you: Which one of the following statements is correct?
(a)
If 2=log
10
(100), it means that 10
2
= 100
(b)
If 2=log
10
(100), it means that 2
10
= 100
(c)
If 2=log
10
(100), it means that 100
10
= 2
Check one of
(a)
to
(c)
.
Q3.
You think this is easy, heh? Try this one then: Which equation is correct?
(a)
10
-2
= 1/(10
2
) = 1/100 = 0.01
(b)
10
-2
= 10
2
= 100
(c)
10
-2
= log
10
(100)
Check one of
(a)
to
(c)
.
Q4.
Now try this: Which one of the equations is correct?
(a)
ln(24*56) = ln(24) * ln(56)
(b)
ln(24*56) = ln(24) + ln(56)
(c)
ln(24*56) = ln(24) - ln(56)
Check one of
(a)
to
(c)
.
Q5.
And what about this one:
(a)
ln(2
5
) = 2 ln(5)
(b)
ln(2
5
) = ln(2) + ln(5)
(c)
ln(2
5
) = 5 ln(2)
Check one of
(a)
to
(c)
.
Q6.
Now let's see: What is the derivative of the function
y
= ln(
x
) ?
(a)
y
' = 1/
x
(b)
y
' =
x
2
(c)
y
' = log
10
(
x
)
Check one of
(a)
to
(c)
.
Q7.
If you knew this one, then let's make it more difficult: Find the derivative of
y
= 2 ln(
x
) +
x
2
(a)
y
' = 1/
x
+
x
2
(b)
y
' = 1/(2
x
)
(c)
y
' = 2/
x
+ 2
x
= 2 (1/
x
+ x)
Check one of
(a)
to
(c)
.
Q8.
Even a bit more difficult: Find the derivative of
y
= ln(3
x
)
(a)
y
' = 1/
x
(b)
y
' =
x
2
(c)
y
' = 3
x
Check one of
(a)
to
(c)
.
Q9.
And more difficult: What's the derivative of
y
= ln(3
x
2
)?
(a)
y
' = 2 ln(3
x
)
(b)
y
' = 6/
x
2
(c)
y
' = 2/
x
Check one of
(a)
to
(c)
.
Q10.
Right. Now what is the approximate value of the mysterious number
e
?
(a)
e
= 2.718281828...
(b)
e
= 3.14159265...
(c)
e
= 1.414213562...
Check one of
(a)
to
(c)
.
Q11.
Can you find the value of this: ln(
e
7
) without using your calculator?
(a)
7
(b)
1
(c)
100.000
Check one of
(a)
to
(c)
.
Q12.
And of this: ln(
e
3
) + ln(
e
2
) ?
(a)
4
(b)
5
(c)
6
Check one of
(a)
to
(c)
.
Q13.
And can you find the value for
x
in this equation: 10
x
= 0.001
(a)
-1
(b)
-2
(c)
-3
Check one of
(a)
to
(c)
.
Q14.
And here: 2
x
= 1024
(a)
10
(b)
-10
(c)
0
Check one of
(a)
to
(c)
.
Q15.
Finally: Why is the exponential function,
y
=
a
x
, very important?
(a)
Because it is a very complicated function
(b)
Because it is always positive
(c)
Because it describes many processes in nature and society
Check one of
(a)
to
(c)
.
Quiz devised by Gisle Kleppe, e-mail
gisle.kleppe@hsh.no
.
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script
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on 14 September 2001 at 13:01