Cambridge Additional Mathematics

Logarithms (Chapter 5) 153

2 Find:

a lg

p

10 b lg

1

p 310 c lg(10

a£ 10 b+1)

3 Simplify:

a 4 ln 2 + 2 ln 3 b^12 ln 9¡ln 2 c 2ln5¡ 1 d^14 ln 81

4 Find:

a ln(e

p

e) b ln

³ 1

e^3

́

c ln(e^2 x) d ln

³e

ex

́

5 Write as a single logarithm:

a lg 16 + 2 lg 3 b log 216 ¡2 log 23 c 2 + log 45

6 Write as logarithmic equations:

a P=3£ 7 x b m=

n^3

5

7 Solve forx:

a log 2 (x+5)¡log 2 (x¡2) = 3 b lgx+lg(x+ 15) = 2

8 Show that log 37 £2 log 7 x= 2 log 3 x.

9 Write the following equations without logarithms:

a lgT=2lgx¡lg 5 b log 2 K=x+ log 23

10 Write in the form alnk whereaandkare positive whole numbers andkis prime:

a ln 32 b ln 125 c ln 729

11 Copy and complete: Function y= log 2 x y=ln(x+5)

Domain

Range

12 If A= log 52 and B= log 53 , write in terms ofAandB:

a log 536 b log 554 c log 5 (8

p

3) d log 5 (20:25) e log 5 (0:8)

13 Solve forx:

a 3 ex¡5=¡ 2 e¡x b 2lnx¡3ln

³

1

x

́

=10

14 Solve forx, giving your answer to 2 decimal places:

a 7 x= 120 b 6 £ 23 x= 300

15 A population of seals is given by P=20£ 2

t

(^3) wheretis the time in years, t> 0.
Find the time required for the population to reach 100.
16 Consider f:x 7! 5 e¡x+1.
a State the range off.
b Find: i f¡^1 (x) ii f¡^1 (2)
c State the domain off¡^1.
d Solve f¡^1 (x)=0.
e Sketch the graphs off,f¡^1 , and y=x on the same set of axes.
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Y:\HAESE\CAM4037\CamAdd_05\153CamAdd_05.cdr Tuesday, 21 January 2014 2:50:19 PM BRIAN