Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | 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.
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Since we have substituted , therefore;
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Taking natural logarithm of both sides in both equations. |
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Power Rule; |
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Power Rule; |
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Hence;
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