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Exponential and Logarithmic Functions - Solving Logarithm Equations

Exponential and Logarithmic Functions - Solving Logarithm Equations

Secondary 4
7 marks
  1. State the range of values of \(x\) for which the equation below is valid. \[ 2\log_3(4-x)-\log_9(x-4)^2=2 \][1]
  2. Express \(2\log_3(4-x)-\log_9(x-4)^2=2\) as a quadratic equation \(x^2+bx+c=0\) and explain why the original logarithmic equation has only one real solution.[6]

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Answer:(a) \(x<4\) (b) \(x^2-8x-65=0\), with \(x=-5\) only.

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