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

$${\mathbf{log}}_2\mathit{x}\times {\mathbf{log}}_4\mathit{x}\times {\mathbf{log}}_{16}\mathit{x}=7$$$$\mathit{h}\mathit{e}\mathit{l}\mathit{p}$$

Answered by MJS last updated on 08/Apr/18

$${\log }_{2}x\times \frac{1}{2}{\log }_{2}x\times \frac{1}{4}{\log }_{2}x=7$$$$\frac{1}{8}{\left({\log }_{2}x\right)}^3=7$$$${\log }_{2}x=2\sqrt[3]{7}$$$$x=2^{2\sqrt[3]{7}}=4^{\sqrt[3]{7}}\approx 14.18075$$

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