Logarithmic equation with a change of base, solved for x in terms of the base
Logarithmic equation with a change of base, solved for x in terms of the base
5 marks
The positive real numbers \(b\) and \(x\), where \(b\ne1\) and \(x>1\), satisfy the equation
\[\log_b(x^3)+\log_{b^2}(x^4)=2(\log_b x)^2\]
Express \(x\) in terms of \(b\).[5]
Solution:
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Answer:\(x=b^{\frac52}\) (which requires \(b>1\))
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