Exponential or logarithmic inequality

Solve inequalities involving exponential expressions like aˣ < b or combined with absolute values.

2 questions · Moderate -0.2

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CAIE P2 2005 November Q1
3 marks Moderate -0.8
1 Solve the inequality \(( 0.8 ) ^ { x } < 0.5\).
OCR MEI AS Paper 1 2020 November Q11
9 marks Standard +0.3
11 In this question you must show detailed reasoning.
  1. A student is asked to solve the inequality \(x ^ { \frac { 1 } { 2 } } < 4\). The student argues that \(x ^ { \frac { 1 } { 2 } } < 4 \Leftrightarrow x < 16\), so that the solution is \(\{ x : x < 16 \}\).
    Comment on the validity of the student's argument.
  2. Solve the inequality \(\left( \frac { 1 } { 2 } \right) ^ { x } < 4\).
  3. Show that the equation \(2 \log _ { 2 } ( x + 8 ) - \log _ { 2 } ( x + 6 ) = 3\) has only one root.