Math 1090
Quiz 5
March 30, 2015
Answer the following questions in the space provided. The value of every
question is indicated at the beginning. Time: 12 minutes.
Name:
1. Graph the following functions
(a) (4 points) f (x) = ex
(b) (4 points) f (x) = 1 + ex−1
(c) (4 points) f (x) = 1 − e−x
Below you can see all three graphs together:
UID:
2.
(i) (4 points) Condense the expression 2 log25 (x) − log25 (x − 2)2 .
Solution.
2
2 log25 (x) − log25 (x − 2)
2
2
= log25 (x ) − log25 (x − 2) = log25
2
x
= log25
x−2
x2
(x − 2)2
(ii) (4 points) Solve the equation 2 log25 (x) − log25 (x − 2)2 = 1.
Solution. In part (i) we have seen that the left hand side can be written as
2
x
log25 x−2
so our equation becomes
log25
x
x−2
2
=1
There are two equivalent ways to proceed now. You can start be bringing the square
to the front and then proceed as follows
2
x
log25
=1
x−2
x
=1
2 log25
x−2
x
1
log25
=
x−2
2
x
251/2 =
x−2
x
5=
x−2
x = 5(x − 2)
0 = 5x − 10 − x
10
5
x=
=
4
2
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You can also leave the square where it is and apply the definition of the logarithm
at the beginning
2
x
log25
=1
x−2
2
x
1
25 =
x−2
x
251/2 =
x−2
This is the same equation we encountered before (4th line), so we may conclude
analogously.
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