Cambridge International Mathematics

Consider two positive numbersxandy. We can write them both with basea: x=ap and y=aq, for somepandq. ) p= logax and q= logay ... ...

EXERCISE 31C 1 Write as a single logarithm: a log 3 2 + log 38 b log 29 ¡log 23 c 3 log 5 2 + 2 log 53 d log 3 8 + log 37 ¡log 3 ...

2 Copy and complete: Number Number as a power of 10 logof number p 10 p (^310) p 1000 p^1 10 3 Can you draw any conclusion from ...

EXERCISE 31D.1 1 a 8 b 80 c 800 d 0 : 8 e 0 : 008 f 0 : 3 g 0 : 03 h 0 :000 03 i 50 j 0 : 0005 2 Write as a single logarithm in ...

Example 9 Self Tutor Write these equations without logarithms: a logD=2x+1 b logN¼ 1 : 301 ¡ 2 x a logD=2x+1 ) D=10^2 x+1 or D= ...

We have already seen how to solve equations such as 2 x=5using technology. We now consider an algebraic method. By definition, t ...

To solve logarithmic equations, we can sometimes write each side as a power of 10. Example 13 Self Tutor Solve forx: log 3 x=¡ 1 ...

Review set 31A #endboxedheading 1aOn the same set of axes, sketch the graphs of y=2x and y= log 2 x. b What transformation would ...

Review set 31B #endboxedheading 1aOn the same set of axes, sketch the graphs of y=3x and y= log 3 x. b State the domain and rang ...

Challenge #endboxedheading 1 Where is the error in the following argument? 1 2 > 1 4 ) log(^12 )>log(^14 ) ) log(^12 )> ...

Inequalities 32 Contents: A Solving one variable inequalities with technology [2.2] B Linear inequality regions [7.7] C Integer ...

² if we want to findxsuch that f(x)< 0 , we graph y=f(x)and find values ofxwhere the function isbelow thex-axis ² if we want ...

Linear inequalitiesdefine regions of the Cartesian plane. Example 3 Self Tutor Write inequalities to represent the following uns ...

Discovery Linear inequalities of the form ax+by < d or ax+by > d #endboxedheading Consider the regions on either side of t ...

EXERCISE 32B 1 Write inequalities to represent the following unshaded regions, abc de f gh i 2 Graph the regions defined by: a x ...

In many problems involving inequalities, the only points which are possible are those with integer coordinates. We therefore con ...

EXERCISE 32C This section is an extension to the syllabus item7.7and is a good example ofmathematical modelling. In some problem ...

EXERCISE 32D 1 4 litre cans of base white paint are converted into lime green or pine green by adding yellow tint and blue tint ...

d Determine how many of each set the manufacturer should make each hour to maximise the profit. e Are any components under-utili ...

a Copy and complete the table: Meter Gears Dials Assembly time (min) Profit Number Gas x Water y b Construct five constraints in ...