Rational exponential equation

Solve equations where exponentials appear in fractions, such as (a^x + p)/(a^x + q) = k, by first finding a^x algebraically.

3 questions · Moderate -0.5

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CAIE P2 2020 November Q2
5 marks Moderate -0.3
2 Given that \(\frac { 2 ^ { 3 x + 2 } + 8 } { 2 ^ { 3 x } - 7 } = 5\), find the value of \(2 ^ { 3 x }\) and hence, using logarithms, find the value of \(x\) correct to 4 significant figures.
CAIE P3 2010 June Q1
4 marks Moderate -0.8
1 Solve the equation $$\frac { 2 ^ { x } + 1 } { 2 ^ { x } - 1 } = 5$$ giving your answer correct to 3 significant figures.
CAIE P2 2016 November Q2
5 marks Moderate -0.3
2
  1. Given that \(\frac { 1 + 4 ^ { y } } { 3 + 2 ^ { y } } = 5\), find the value of \(2 ^ { y }\).
  2. Use logarithms to find the value of \(y\) correct to 3 significant figures.