© Cengage Learning Australia Pty Ltd 2014 MAT10NAWK10212 Number and Algebra: Real numbers www.nelsonnet.com.au 1 of 3 1 Evaluate each expression. a log 10 1000 _______ b log 2 256 _______ c log 5 125 _______ d log 7 49 _______ e log 6 1 6 _______ f log 8 1 64 _______ g log 9 3 _______ h log 3 1 _______ 2 Write each equation in logarithmic form. a 4 3 5 64 _________ b 5 2 5 25 _________ c 2 r 5 32 _________ d y 6 5 z _________ 3 Write each equation in index form. a log 10 100 5 2 _______ b log 2 8 5 3 _______ c log 3 b 5 7 _______ d log a 16 5 2 _______ 4 Simplify and evaluate each expression. a log 3 3 5 _________ b log 4 32 1 log 4 2 _________ c log 10 900 2 log 10 9 _________ d 3log 6 2 1 log 6 27 _________ e log 5 15 1 log 5 2 2 log 5 6 _________ f 3log 10 5 2 log 10 2 1 log 10 16 _________ g log 9 12 2 2log 9 2 _________ h 2log 2 4 1 log 2 20 2 1 2 log 2 25 _________ 5 Simplify each expression. a log a 5 1 log a 6 _________ b log a 25 2 log a 5 _________ c log a 6 1 log a 8 2 log a 4 _________ d log a 4a 2 _________ e log a 20 2 (log a 5 1 log a 4) _________ f log a 6a 2 2 log a 2a 4 _________ g 1 2 log a 16a _________ h log a 3c 1 1 3 log a d 2 2log a e _________ 6 Expand each expression. a log a (xy) _________ b log a (x n ) _________ c log a pq r _________ d log a (4s 2 ) _________ e log a xy _________ f log a c d 2 _________ 7 If log n 4 5 x, log n 6 5 y and log n 10 5 z, express each of the following in terms of x, y and z. a log n 40 _________ b log n 2 _________ c log n 160 _________ d log n 15 _________ Logarithms review WORKSHEET

Worksheet Logarithms reviewweb2.hunterspt-h.schools.nsw.edu.au/studentshared/MATHEMATICS/Year... · 32 5 r d log y z 5 6 3 a 102 5 100 b 23 5 8 c 37 5 b d a2 5 16 4 a 5 b 3 c 2 d

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Page 1: Worksheet Logarithms reviewweb2.hunterspt-h.schools.nsw.edu.au/studentshared/MATHEMATICS/Year... · 32 5 r d log y z 5 6 3 a 102 5 100 b 23 5 8 c 37 5 b d a2 5 16 4 a 5 b 3 c 2 d

1 of 3

1 Evaluate each expression.

a log101000 _______ b log2256 _______ c log5125 _______ d log749 _______

e log6

_______ f log8

164

_______ g log93 _______ h log31 _______

2 Write each equation in logarithmic form.

a 43 5 64 _________ b 52 5 25 _________ c 2r 5 32 _________ d y6 5 z _________

3 Write each equation in index form.

a log10100 5 2 _______ b log28 5 3 _______ c log3b 5 7 _______ d loga16 5 2 _______

4 Simplify and evaluate each expression.

a log335 _________ b log432 1 log42 _________

c log10900 2 log109 _________ d 3log62 1 log627 _________

e log 515 1 log52 2 log56 _________ f 3log105 2 log102 1 log1016 _________

g log 912 2 2log92 _________ h 2log24 1 log220 2 12

log225 _________

5 Simplify each expression.

a log a 5 1 loga6 _________ b loga25 2 loga5 _________

c loga6 1 loga8 2 loga4 _________ d loga4a2 _________

e loga20 2 (loga5 1 loga4) _________ f loga6a2 2 loga2a4 _________

g 12

loga16a _________ h loga3c 1 13

logad 2 2logae _________

6 Expand each expression.

a loga(xy) _________ b loga(xn) _________ c loga

pqr

_________

d loga(4s2) _________ e loga xy _________ f loga

cd2 _________

7 If logn4 5 x, logn6 5 y and logn10 5 z, express each of the following in terms of x, y and z.

a logn40 _________ b logn2 _________ c logn160 _________ d logn15 _________

Logarithms review

Worksheet

MAT10NAWK10212.indd 1 14/06/14 12:00 PM

2 of 3

8 If log106 5 0.7782, find the value of each expression.

a log1036 _________ b log 1016

_________ c log 10 60 _________

d log100.6 _________ e log 10360 _________ f log 10 6000 _________

9 Solve each equation, correct to two decimal places where necessary.

a 4x5 4096 _________ b 6x 5 1 679 616 _________ c 5x 5 120 _________

d 2x 1 2 5 3264 _________ e 4x 2 3 5 1984 _________ f 34 2 x 5 300 _________

10 Solve each equation.

a log 3 x 5 4 _________ b log 5 x 5 5 _________ c log 4 x 5 12

_________

d log x 36 5 2 _________ e log x1

10 5 21 _________ f log x 64 5 3 _________

MAT10NAWK10212.indd 2 14/06/14 12:00 PM

Page 3: Worksheet Logarithms reviewweb2.hunterspt-h.schools.nsw.edu.au/studentshared/MATHEMATICS/Year... · 32 5 r d log y z 5 6 3 a 102 5 100 b 23 5 8 c 37 5 b d a2 5 16 4 a 5 b 3 c 2 d

3 of 3

Answers 1 a 3 b 8 c 3 d 2

e 21 f 22 g 12

h 0

2 a log 4 64 5 3 b log 5 25 5 2 c log 2 32 5 r d log y z 5 6 3 a 102 5 100 b 23 5 8 c 37 5 b d a2 5 16 4 a 5 b 3 c 2 d 3

e 1 f 3 g 12

h 6

5 a log a 30 b log a 5 c log a 12 d log a 4 1 2

e 0 f log a 3 2 2 g log a 4 1 12

h log a

c de

3 3

6 a log a x 1 log a y b nlog a x c log a p 1 log aq 2 log ar

d log a 4 1 2log a 5 e 12

log a x 1 12

log a y f log a c 2 2log a d

7 a x 1 z b 12

x c 2x 1 z d y 1 z 2 x

8 a 1.5564 b 20.7782 c 1.7782 d 20.2218 e 2.5564 f 1.8891 9 a x 5 6 b x 5 8 c x < 2.97 d x < 9.67 e x < 8.48 f x < 21.1910 a x 5 81 b x 5 3125 c x 5 2 d x 5 6 e x 5 10 f x 5 4x

MAT10NAWK10212.indd 3 14/06/14 12:00 PM

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