Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2002  OctNov  (P29709/02)  Q#3
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Question
i. Express in terms of y, where
ii. Hence solve the equation
expressing your answers for x in terms of logarithms where appropriate.
Solution
i.
We are given that , therefore;
Hence, where .
ii.
We are required to solve the equation;
Let’s substitute ;
As demonstrated in (i), when , therefore;
It is evident that now we have a quadratic equation to solve.
For a quadratic equation , the expression for solution is;
Therefore;
Now we have two options.






Since we have substituted , therefore;


Taking natural logarithm of both sides in both equations. 



Power Rule;










Power Rule;





Hence;


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