Cambridge Additional Mathematics

154 Logarithms (Chapter 5)

Review set 5B

#endboxedheading

1 Without using a calculator, find the base 10 logarithms of:

a

p

1000 b

10

p 310 c

10 a

10 ¡b

2 Write in the form 10 xgivingxcorrect to 4 decimal places:

a 32 b 0 : 0013 c 8 : 963 £ 10 ¡^5

3 Findxif:

a log 2 x=¡ 3 b log 5 x¼ 2 : 743 c log 3 x¼¡ 3 : 145

4 Write the following equations without logarithms:

a log 2 k¼ 1 :699 +x b logaQ= 3 logaP+ loga 5 c lgA=xlg 2 + lg 6

5 Solve forx, giving exact answers:

a 5 x=7 b 20 £ 22 x+1= 640

6 Find the exact value of log 123 ¡2 log 126.

7 Write log 830 in the form alog 2 b, where a,b 2 Q.

8 Solve forx:

a log 4 x+ log 4 (2x¡8) = 3 b logx135 = 3 + logx 5

9 Consider f(x)=ex and g(x) = ln(x+4), x>¡ 4. Find:

a (f±g)(5) b (g±f)(0)

10 Write as a single logarithm:

a ln 60¡ln 20 b ln 4 + ln 1 c ln 200¡ln 8 + ln 5

11 Write as logarithmic equations:

a M=5£ 6 x b T=

5

p

l

c G=

4

c

12 Solve exactly forx:

a e^2 x=3ex b e^2 x¡ 7 ex+12=0

13 Consider the function g:x 7 !log 3 (x+2)¡ 2.

a Find the domain and range.

b Find any asymptotes and axes intercepts for the graph of the function.

c Find the defining equation for g¡^1.

d Sketch the graphs of g, g¡^1 , and y=x on the same axes.

14 The weight of a radioactive isotope remaining aftertweeks is given by W= 8000£e

¡ 20 t

grams.

Find the time for the weight to halve.

15 Solve forx:

a log 2 x+ log 4 x^4 = log 2125 b log 2 x= 25 logx 2 c log 3 x+ 8 logx3=6

16 Consider f(x)=5e^2 x and g(x) = ln(x¡4).

a State the domain and range ofg. b Find the axes intercepts ofg.

c Find the exact solution to fg(x)=30. d Solve f(x)=g¡^1 (x).

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_05\154CamAdd_05.cdr Tuesday, 21 January 2014 2:50:22 PM BRIAN