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Question Number 211706 by Nadirhashim last updated on 17/Sep/24

$$\mathit{i}\mathit{f}{\mathit{x}}^{\mathit{l}\mathit{o}\mathit{g}27}+9^{\mathit{l}\mathit{o}\mathit{g}\mathit{x}}=36\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{x}$$

Answered by mehdee7396 last updated on 17/Sep/24

$$x^{3log3}+x^{2log3}=36$$$$x^{log3}=y\Rightarrow y^3+y^2-36=0$$$$(y-3)(y^2+4y+12)=0$$$$ifx\in \mathbb{R}\Rightarrow y=3=x^{log3}\Rightarrow x=10✓$$$$$$

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