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Question Number 158699 by MathsFan last updated on 07/Nov/21

$$\sqrt{({\log }_{3}3\sqrt{3\mathrm{x}}+{\log }_{\mathrm{x}}3\sqrt{3\mathrm{x}}){\log }_3{\mathrm{x}}^3}+\sqrt{(\frac{{\log }_{3}3\sqrt{\mathrm{x}}}{3}+\frac{{\log }_{\mathrm{x}}3\sqrt{\mathrm{x}}}{3}){\log }_3{\mathrm{x}}^3}=2$$$$\mathrm{please}\mathrm{i}\mathrm{need}\mathrm{help}.$$$$\mathrm{Ive}\mathrm{been}\mathrm{trying}\mathrm{but}\mathrm{still}\mathrm{not}\mathrm{getting}$$$$\mathrm{answer}.$$

Commented by MJS_new last updated on 08/Nov/21

$$\mathrm{you}\mathrm{can}\mathrm{only}\mathrm{approximate}\mathrm{I}\mathrm{think}$$

Commented by MJS_new last updated on 08/Nov/21

$$\mathrm{let}x=3^t$$$$\sqrt{\frac{3}{2}{t}^2+6t+\frac{9}{2}}+\sqrt{\frac{1}{2}{t}^2+\frac{3}{2}t+1}=2$$$$\mathrm{squaring}\mathrm{\&}\mathrm{transforming},2\mathrm{times}\mathrm{leads}\mathrm{to}$$$$t^4+9t^3+\frac{45}{4}{t}^2-\frac{57}{2}t-\frac{63}{4}=0$$$$\mathrm{and}\mathrm{this}\mathrm{has}\mathrm{no}‘‘{\mathrm{nice}}^{″}\mathrm{solution}$$

Commented by MathsFan last updated on 08/Nov/21

$$\mathrm{okay}\mathrm{sir}$$$$\mathrm{thanks}$$

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