Solve |exponential| < constant

Solve inequality involving modulus of exponential expression less than constant, e.g. |2^x-8| < 5 or |3^x-8| < 0.5.

5 questions · Standard +0.2

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CAIE P3 2003 November Q1
4 marks Moderate -0.3
1 Solve the inequality \(\left| 2 ^ { x } - 8 \right| < 5\).
CAIE P3 2006 November Q1
4 marks Standard +0.3
1 Find the set of values of \(x\) satisfying the inequality \(\left| 3 ^ { x } - 8 \right| < 0.5\), giving 3 significant figures in your answer.
CAIE P2 2007 November Q3
5 marks Standard +0.3
3
  1. Solve the inequality \(| y - 5 | < 1\).
  2. Hence solve the inequality \(\left| 3 ^ { x } - 5 \right| < 1\), giving 3 significant figures in your answer.
CAIE P3 2023 November Q1
4 marks Standard +0.3
1 Find the set of values of \(x\) satisfying the inequality \(\left| 2 ^ { x + 1 } - 2 \right| < 0.5\), giving your answer to 3 significant figures.
OCR MEI C3 Q3
7 marks Standard +0.3
3 The graph shows part of the function \(y = a \ln ( b x )\). \includegraphics[max width=\textwidth, alt={}, center]{2f403099-2813-40d8-a9ae-1f7e64d41f80-2_377_762_900_685} The graph passes through the points \(( 2,0 )\) and \(( 4,1 )\).
  1. Show that \(b = \frac { 1 } { 2 }\) and find the exact value of \(a\).
  2. Solve the inequality \(| a \ln ( b x ) | < 2\).