Cambridge Additional Mathematics

Logarithms (Chapter 5) 141 Historical note The invention of logarithm #endboxedheading It is easy to take modern technology, suc ...

y 1 x 1 (e 1), (1 e), y=x y=ex y=lnx O 142 Logarithms (Chapter 5) InChapter 4we came across thenatural exponential e¼ 2 :718 28. ...

If then. ln = = xa xea Logarithms (Chapter 5) 143 5 Use your calculator to write the following in the form ek wherekis correct t ...

144 Logarithms (Chapter 5) EXERCISE 5E.2 1 Write as a single logarithm or integer: a ln 15 + ln 3 b ln 15¡ln 3 c ln 20¡ln 5 d ln ...

Logarithms (Chapter 5) 145 5 Write the following equations without logarithms, assuming all terms are positive: a lnD=lnx+1 b ln ...

Logarithms allow us to solve exponential equations even if we cannot write both sides with the same base. 146 Logarithms (Chapte ...

GRAPHING PACKAGE Logarithms (Chapter 5) 147 Example 23 Self Tutor Find algebraically the exact points of intersection of y=ex¡ 3 ...

If , then. 2= = log x a xaw 148 Logarithms (Chapter 5) Example 24 Self Tutor Evaluate log 29 by: a changing to base 10 b changin ...

y 1 x 11 O y=x y=ax y=logz_x (a 1), (_ -1)Qz, y 1 x 11 O y=x y=ax (a 1)(a 1),, (_ -1)Qz, y=logz_x y x (-1 ),Qz^1 (1 a), O Logari ...

-2 2 4 6 8 10 6 4 2 -2 y O x x=1 (2 1), (5 3), y =logw(x - 1) + 1 1_Qw 150 Logarithms (Chapter 5) Example 26 Self Tutor Consider ...

13 x y O A B 1 x y O y =ln(x ) 2 y=lnx y x (1 3), (3 1), O y=x y=ex-3 y=3+lnx Logarithms (Chapter 5) 151 Example 27 Self Tutor C ...

CARD GAME 152 Logarithms (Chapter 5) 5 Consider the function f:x 7 !ex+3+2. a Find the defining equation for f¡^1. b Find the va ...

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 ...

154 Logarithms (Chapter 5) Review set 5B #endboxedheading 1 Without using a calculator, find the base 10 logarithms of: a p 1000 ...

Polynomials 6 Contents: A Real polynomials B Zeros, roots, and factors C The Remainder theorem D The Factor theorem E Cubic equa ...

156 Polynomials (Chapter 6) Opening problem To determine whether 7 is afactorof 56 , we divide 56 by 7. The result is exactly 8. ...

Polynomials (Chapter 6) 157 Example 1 Self Tutor If P(x)=x^3 ¡ 2 x^2 +3x¡ 5 and Q(x)=2x^3 +x^2 ¡ 11 , find: a P(x)+Q(x) b P(x)¡Q ...

158 Polynomials (Chapter 6) EXERCISE 6A.1 1 If P(x)=x^2 +2x+3 and Q(x)=4x^2 +5x+6, find in simplest form: a 3 P(x) b P(x)+Q(x) c ...

Polynomials (Chapter 6) 159 If P(x) is divided by ax+b until a constant remainderRis obtained, then P(x) ax+b =Q(x)+ R ax+b wher ...

160 Polynomials (Chapter 6) Example 5 Self Tutor Perform the division x^4 +2x^2 ¡ 1 x+3 . Hence write x^4 +2x^2 ¡ 1 in the form ...