log-2-x-log-4-x-log-16-x-7-help-

Question Number 32954 by mondodotto@gmail.com last updated on 07/Apr/18

\log_{2} x \times \log_{4} x \times \log_{16} x = 7

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Answered by MJS last updated on 08/Apr/18

\log_{2} x \times \frac{1}{2} \log_{2} x \times \frac{1}{4} \log_{2} x = 7

\frac{1}{8} {(\log_{2} x)}^{3} = 7

\log_{2} x = 2 \sqrt[3]{7}

x = 2^{2 \sqrt[3]{7}} = 4^{\sqrt[3]{7}} \approx 14.18075

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