Cambridge Additional Mathematics

GRAPHING PACKAGE Surds, indices, and exponentials (Chapter 4) 121 EXERCISE 4G 1 Use the graph of y=2x to estimate the value of: ...

bi b iii bii GRAPHING PACKAGE 2 4 6 8 10 12 14 6000 4000 2000 A( )ha n(weeks) 8000 a bi b iii bii 122 Surds, indices, and expone ...

Surds, indices, and exponentials (Chapter 4) 123 We have seen that the simplest exponential functions are of the form f(x)=bx wh ...

124 Surds, indices, and exponentials (Chapter 4) a ³ 1+ 1 a ́a 10 100 1000 10 000 100 000 1 000 000 10 000 000 4 For continuous ...

CARD GAME Surds, indices, and exponentials (Chapter 4) 125 4 Consider y=2ex. a Explain whyycan never be< 0. b Findyif: i x=¡ ...

126 Surds, indices, and exponentials (Chapter 4) 4 Let f(x)=3x. a Write down the value of: i f(4) ii f(¡1) b Find the value ofks ...

-1 1 x y= 3 x y 1 4 O Surds, indices, and exponentials (Chapter 4) 127 15 The temperature of a dishtminutes after it is removed ...

128 Surds, indices, and exponentials (Chapter 4) 10 Expand and simplify: a ex(e¡x+ex) b (2x+5)^2 c (x 1 (^2) ¡7)(x 1 (^2) +7) 11 ...

Logarithms 5 Contents: A Logarithms in base B Logarithms in base C Laws of logarithms D Logarithmic equations E Natural logarith ...

130 Logarithms (Chapter 5) Opening problem In a plentiful springtime, a population of 1000 mice will double every week. The popu ...

Logarithms (Chapter 5) 131 Numbers like p 10 , 10 p 10 and 1 p 510 can also be written in the form 10 x as follows: p 10 = 10 1 ...

132 Logarithms (Chapter 5) Example 2 Self Tutor Use your calculator to write the following in the form 10 x wherexis correct to ...

Logarithms (Chapter 5) 133 8 Findxif: a lgx=2 b lgx=1 c lgx=0 d lgx=¡ 1 e lgx=^12 f lgx=¡^12 g lgx=4 h lgx=¡ 5 i lgx¼ 0 : 8351 j ...

134 Logarithms (Chapter 5) EXERCISE 5B 1 Write an equivalent exponential equation for: a log 10 100 = 2 b log 10 10 000 = 4 c lo ...

Logarithms (Chapter 5) 135 Discussion #endboxedheading We have seen that p 2 cannot be written in the form p q where p,q 2 Z, q ...

136 Logarithms (Chapter 5) More generally, in any basecwhere c 6 =1, c> 0 , we have theselaws of logarithms: IfAandBare both ...

Logarithms (Chapter 5) 137 EXERCISE 5C 1 Write as a single logarithm or as an integer: a lg 8 + lg 2 b lg 4 + lg 5 c lg 40¡lg 5 ...

^ 02 0 222 222 : : :::: means 138 Logarithms (Chapter 5) 6 If x= log 2 P, y= log 2 Q, and z= log 2 R, write in terms ofx,y, andz ...

Logarithms (Chapter 5) 139 Example 11 Self Tutor Write the following equations without logarithms: a lgy=xlg 4 + lg 3 b log 2 M= ...

140 Logarithms (Chapter 5) SOLVING LOGARITHMIC EQUATIONS Logarithmic equations can often be solved using the laws of logarithms. ...