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Question Number 32960 by mondodotto@gmail.com last updated on 08/Apr/18

$${\mathbf{log}}_2\mathit{x}+{\mathbf{log}}_4\mathit{x}+{\mathbf{log}}_{16}\mathit{x}=7$$

Answered by Joel578 last updated on 08/Apr/18

$${\log }_{a^n}{b}^m=\frac{m}{n}{\log }_{a}b$$$$$$$${\log }_{2}x+{\log }_{2^2}x+{\log }_{2^4}x=7$$$${\log }_{2}x+\frac{1}{2}{\log }_{2}x+\frac{1}{4}{\log }_{2}x=7$$$$\frac{7}{4}{\log }_{2}x=7$$$${\log }_{2}x=4$$$$x=2^4=16$$

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