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Exponential and logarithmic equations solved as quadratics by substitution

Exponential and logarithmic equations solved as quadratics by substitution

8 marks

Find the exact solutions of each of the following equations.

  1. \(e^x-15e^{-x}=2\)[4]
  2. \(\ln x-\dfrac{15}{\ln x}=2\)[4]

Solution:

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Answer:(a) \(x=\ln5\) (b) \(x=e^5\) or \(x=e^{-3}\)

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