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Change of base to simplify a base-8 logarithm and the exact solution of a related logarithmic equation

Change of base to simplify a base-8 logarithm and the exact solution of a related logarithmic equation

7 marks
  1. For \(x>0\), show that \(\log_8\left(27x^3\right)=\log_2 3+\log_2 x\).[4]
  2. Hence solve \(\log_2\sqrt{x}=\log_8\left(27x^3\right)-\log_2 6\) for \(x>0\).[3]

Solution:

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Answer:(a) shown (b) \(x=4\)

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