Name: 
 

Chapter 1: Logarithmic functions


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Simplify log2 (12) + log2 (3) – log2 (6).
A
log2 (9)
B
2 log2 (3)
C
log2 (6)
D
6
E
9
 

 2. 
Simplify log3 mc002-1.jpg.
A
mc002-2.jpg
B
mc002-3.jpg
C
mc002-4.jpg
D
mc002-5.jpg
E
mc002-6.jpg
 

 3. 
Use the change of base theorem to calculate log9 (4) correct to four decimal places.
A
0.5219
B
0.5543
C
0.5695
D
0.6020
E
0.6309
 

 4. 
Solve 52x–1 + 5 = 130.
A
x = 0
B
x = 1
C
x = 2
D
x = 3
E
x = 4
 

 5. 
Solve 22x+5 = 4mc005-1.jpg.
A
x = mc005-2.jpg
B
x = mc005-3.jpg
C
x = mc005-4.jpg
D
x = mc005-5.jpg
E
x = mc005-6.jpg
 

 6. 
Solve mc006-1.jpg = 27.
A
x = 2
B
x = 2 or x = 1
C
x = 3
D
x = 3 or x = 1
E
x = 3 or x = –9
 

 7. 
Use logarithms to solve the equation 7x = 9. Answer correct to three decimal places.
A
mc007-1.jpg0.894
B
mc007-2.jpg1.129
C
mc007-3.jpg1.141
D
mc007-4.jpg1.257
E
mc007-5.jpg1.312
 

 8. 
Plot a graph to solve mc008-1.jpg = 2.2.
A
x » 19.8
B
x » 21.1
C
x » 21.9
D
x » 22.4
E
x » 22.9
 

 9. 
Sketch the graph of y = –mc009-1.jpg, showing all relevant features.
A
Asymptote: x = 1, zero: x = 2
As x ® 1, y ® ¥.
No y-intercept
mc009-2.jpg
B
Asymptote: x = 1, zero: x = 2
As x ® 1, y ® –¥.
No y-intercept
mc009-3.jpg
C
Asymptote: x = –1, zero: x = 0
As x ® –1, y ® ¥.
y-intercept 0
mc009-4.jpg
D
Asymptote: x = –1, zero: x = 0
As x ® –1, y ® –¥.
y-intercept 0
mc009-5.jpg
E
Asymptote: x = 1, zero: x = 2
As x ® 1, y ® ¥.
No y-intercept
mc009-6.jpg
 

 10. 
Solve the equation log (5x + 1) = 2.
A
x = 1.8
B
x = 19.8
C
x = 20
D
x = 20.2
E
x = 200
 

 11. 
Solve   log2 (x + 10) + log2 (x + 9) = log2 (20).
A
x = –2 or x = –10
B
x = –2
C
x = –5 or x = –14
D
x = –5
E
No solution
 

 12. 
Solve mc012-1.jpg = 2.1.
A
x » 17.2
B
x » 17.5
C
x » 17.9
D
x » 18.2
E
x » 18.4
 

 13. 
For a logarithmic (base 10) scale, how many times bigger is a measurement of 2.8 compared to a measurement of 0.8?
A
2
B
3.5
C
10
D
100
E
1000
 

 14. 
One of the Richter formulas used to measure the magnitude of an earthquake is
M(x) = mc014-1.jpg
x0 is defined as an earthquake with a seismographic reading of 0.001 seismograms at a distance of 100 kilometres from the epicentre.

A seismometer measures an earthquake as 7434 seismograms, calculated for 100 km from the epicentre. What is its magnitude on the Richter scale? Round your answer to one decimal place.
A
5.6
B
6.0
C
6.4
D
6.9
E
7.3
 

 15. 
William invests $12 200 at 9% p.a. compound interest over three years. How much money will he have at the end of the three years? Round your answer to the nearest dollar.
A
$13 689
B
$14 409
C
$15 167
D
$15 799
E
$16 539
 

 16. 
How much, to the nearest dollar, must be invested at 8.5% compound interest over three years, compounded fortnightly, to amount to $7500?
A
$5641
B
$5815
C
$6048
D
$6290
E
$6340
 



 
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