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Change of base to simplify a logarithm, then solving a logarithmic equation

Change of base to simplify a logarithm, then solving a logarithmic equation

IB Year 6 | Grade 12
7 marks
  1. Show that, for \(x>0\), \(\log_4(49x^6)=\log_2 7+3\log_2 x\).[4]
  2. Hence, find the value of \(x\), where \(x>0\), satisfying \(\log_2\sqrt{x}=\log_4(49x^6)+\log_2\frac{32}{7}\).[3]

Solution:

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Answer:(b) \(x=\frac14\)

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