Solve exponential equation using logarithms

Equation of form a^x = b, solved by taking logarithms of both sides and applying log laws.

7 questions · Moderate -0.7

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CAIE P2 2015 June Q1
4 marks Moderate -0.8
  1. Use logarithms to solve the equation \(2^x = 20^5\), giving the answer correct to 3 significant figures. [2]
  2. Hence determine the number of integers \(n\) satisfying $$20^{-5} < 2^n < 20^5.$$ [2]
OCR MEI C2 2006 June Q9
4 marks Moderate -0.8
Use logarithms to solve the equation \(5^{3x} = 100\). Give your answer correct to 3 decimal places. [4]
OCR MEI C2 2008 June Q9
3 marks Moderate -0.8
Use logarithms to solve the equation \(5^x = 235\), giving your answer correct to 2 decimal places. [3]
OCR MEI C2 2014 June Q10
4 marks Moderate -0.3
Use logarithms to solve the equation \(3^{x+1} = 5^{2x}\). Give your answer correct to 3 decimal places. [4]
OCR H240/03 2018 December Q1
3 marks Moderate -0.8
Use logarithms to solve the equation \(2^{3x-1} = 3^{x+4}\), giving your answer correct to 3 significant figures. [3]
OCR H240/01 2017 Specimen Q5
4 marks Moderate -0.3
In this question you must show detailed reasoning. Use logarithms to solve the equation \(3^{2x+1} = 4^{100}\), giving your answer correct to 3 significant figures. [4]
Pre-U Pre-U 9794/1 2010 June Q1
3 marks Easy -1.2
Solve the equation \(2^x = 4^{2x+1}\). [3]