log-12-x-x-1-4-log-9-x-x-

Question Number 129451 by bemath last updated on 15/Jan/21

\log_{12} (\sqrt{x} + \sqrt[4]{x}) = \log_{9} (\sqrt{x})

x = ?

Answered by liberty last updated on 16/Jan/21

\log_{12} (\sqrt{x} + \sqrt[4]{x}) = \log_{3} (\sqrt[4]{x})

let x = t^{4} \Rightarrow \frac{\ln (t^{2} + t)}{\ln 12} = \frac{\ln (t)}{\ln 3}

\ln 3 . \ln (t^{2} + t) = \ln 12 . \ln (t)

\ln 3 . \ln (t^{2} + t) = (\ln 3 + \ln 4) . \ln (t)

holds for t = 3; then x = 3^{4} = 81

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