If log2⁡x+log4⁡x+log16⁡x=214 then x equals

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If $\log_{2} x + \log_{4} x + \log_{16} x = \frac{21}{4}$ then x equals

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Detailed Solution

$\begin{array}{l} \log_{2} x + \log_{4} x + \log_{16} x = \frac{21}{4} \\ \log_{2} x + \frac{1}{2} \log_{2} x + \frac{1}{4} \log_{2} x = \frac{21}{4} \\ (\log_{2} x) (1 + \frac{1}{2} + \frac{1}{4}) = \frac{21}{4} \\ (\log_{2} x) (\frac{7}{4}) = \frac{21}{(4)} \\ \log_{2} x = 3 \Rightarrow x = 2^{3} = 8 \end{array}$