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Question Number 147566 by mathdanisur last updated on 21/Jul/21

$$x^3+3367=2^{\mathit{n}}\Rightarrow x;n=?$$

Answered by Olaf_Thorendsen last updated on 21/Jul/21

$$x^3+3367=2^n$$$$\mathrm{Solution}\mathrm{for}x\in \mathbb{N}.$$$$$$$$x=\sqrt[3]{2^n-3367}$$$$n⩽11\Rightarrow 2^n-3367<0$$$$$$$$n=12:$$$$x=\sqrt[3]{2^{12}-3367}$$$$x=\sqrt[3]{2^n-3367}$$$$x=\sqrt[3]{729}=\sqrt[3]{9^3}=9$$$$\Rightarrow x=9,n=12\mathrm{is}\mathrm{a}\mathrm{solution}$$

Commented by mathdanisur last updated on 22/Jul/21

$$thankyouSir$$

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