Exponential inequality

Solve inequalities involving exponential expressions, such as a^(f(x)) < b^(g(x)), using logarithms.

2 questions · Standard +0.3

1.06g Equations with exponentials: solve a^x = b
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CAIE P3 2020 June Q1
4 marks Standard +0.3
1 Find the set of values of \(x\) for which \(2 \left( 3 ^ { 1 - 2 x } \right) < 5 ^ { x }\). Give your answer in a simplified exact form. [4]
OCR C2 2007 January Q9
10 marks Standard +0.3
On its first trip between Maltby and Grenlish, a steam train uses 1.5 tonnes of coal. As the train does more trips, it becomes less efficient so that each subsequent trip uses 2% more coal than the previous trip.
  1. Show that the amount of coal used on the fifth trip is 1.624 tonnes, correct to 4 significant figures. [2]
  2. There are 39 tonnes of coal available. An engineer wishes to calculate \(N\), the total number of trips possible. Show that \(N\) satisfies the inequality $$1.02^N < 1.52.$$ [4]
  3. Hence, by using logarithms, find the greatest number of trips possible. [4]