MATH 1090 Algebra and Trigonometry
Quiz 4 - Solutions
2002 Winter
Note: if you see symbols like ³ or
Þ in various places, then the Symbol or WP MathA font is not installed
on your computer. The translation is:
- = - (minus)
|
Þ = Þ
(implies) |
-
- Find the value of x , correct to three decimal places,
given that x is the solution of the equation
e2x - 2
= 125
e2x = 125 + 2
= 127
Þ
2x = ln 127
Þ
x = (ln 127) / 2
The decimal approximation of this exact value is
- Solve the equation
log2(x+3) +
log2(x-3)
= 4
log2((x+3)(x-3))
= 4
Þ
(x+3)(x-3)
= 24
Þ
x2 - 9
= 16
Þ
x2 = 25
Þ
x = ±5
But log2(-5+3)
is not real.
log2(+5-3) and
log2(+5+3) are both real.
-5 must be excluded from the solution set,
which is therefore
[Note: the possibility x =
-5 must be stated and excluded
explicitly, in order to receive full credit for this solution.]
- Find the exact value, in simplified form, of
Therefore
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Created 2002 03 28 and modified 2002 03 28 by
Dr. G.H. George.