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Transcript
Name: __________________________ Date: _____________
1. Use a graphing utility to graph the function.
A)
B)
C)
D)
E)
Page 1
2. Identify the x-intercept of the function y = 5 + log 2 x .
A) 32
B) 1
32
C) –5
D) 10
E) The function has no x-intercept.
3. Evaluate the function f ( x) = − 2.504 ln x at x = 182.55 . Round to 3 decimal places. (You may use
your calculator.)
A) –6.125
B) 13.038
C) –13.038
D) 2.079
E) undefined
4.
Rewrite the logarithmic equation log 6
A)
636 = – 2
B)
61/ 36 = – 2
1
6 –2 =
36
C)
D)
⎛ 1 ⎞
⎜ ⎟
⎝ 36 ⎠
E)
6 –2 = −
–2
1
= – 2 in exponential form.
36
=6
1
36
Page 2
5. The pH of an acidic solution is a measure of the concentration of the acid particles in the solution,
with smaller values of the pH indicating higher acid concentration. In a laboratory experiment, the
pH of a certain acid solution is changed by dissolving over-the-counter antacid tablets into the
solution. In this experiment, the pH changes according to the equation
⎛ x ⎞
pH = 5.0 + log ⎜
⎟,
⎝ 0.1 − x ⎠
where x is the number of grams of antacid added to the solution. Use a graphing utility to graph the
pH function on the interval 0 < x < 0.1.
A)
B)
C)
D)
Page 3
E)
6. Write the exponential equation e5 / 2 = 12.1825... in logarithmic form.
A)
⎛5⎞
2.303log ⎜ ⎟ = 12.1825...
⎝2⎠
B)
5
log10 (12.1825...) =
2
C)
5
⎛ ⎞
ln ⎜ ⎟ = 12.1825...
⎝2⎠
D)
5
ln (12.1825...) =
2
E)
12.1825...
ln 5 =
2
7. Identify the the value of the function f ( x) = log 2 .
2
A) 2
B) 102
C) 21/2
D) 1
2
E) undefined
Page 4
8. Write the logarithmic equation ln 5 = 1.609... in exponential form.
A) e1.609... = 5
B)
105 = 1.609...
C)
2.303 e1.609... = 5
D)
2.303 ×105 = 1.609...
E)
e5 = 1.609...
9. Solve the equation log(1 − x) = log(1000) for x using the One-to-One Property.
A) 1001
B) –999
C) –1001
D) –2
E) The equation has no solution.
10. Identify the x-intercept of the function f ( x) = 4 ln( x − 1) .
A) x = 1
B) x = 0
C) x = 4
D) x = 2
E) The function has no x-intercept.
Page 5
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B
B
C
C
E
D
D
A
B
D
Page 6