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Question Number 152571 by Gbenga last updated on 29/Aug/21

$$2\mathit{l}\mathit{o}\mathit{g}{4}^{\mathit{x}}+9{\mathit{l}\mathit{o}\mathit{g}\mathit{x}}^4=9$$$$\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{x}$$

Answered by mr W last updated on 29/Aug/21

$$\log \left(4^{2x}\times x^{36}\right)=9$$$$4^{2x}\times x^{36}={10}^9$$$$2^{\frac{x}{9}}\times x=\pm {10}^{\frac{1}{4}}$$$$e^{\frac{x}{9}\ln 2}\times x=\pm {10}^{\frac{1}{4}}$$$$e^{\frac{x}{9}\ln 2}\times \frac{x\ln 2}{9}=\pm {10}^{\frac{1}{4}}\times \frac{\ln 2}{9}$$$$\frac{x\ln 2}{9}=W(\pm {10}^{\frac{1}{4}}\times \frac{\ln 2}{9})$$$$\Rightarrow x=\frac{9}{\ln 2}W(\pm {10}^{\frac{1}{4}}\times \frac{\ln 2}{9})$$$$=\{\begin{array}{l}\frac{9}{\ln 2}W(-{10}^{\frac{1}{4}}\times \frac{\ln 2}{9})=\{\begin{array}{l}\frac{9}{\ln 2}\times (-3.128713)=-40.624008\\ \frac{9}{\ln 2}\times (-0.160858)=2.088621\end{array}\\ \frac{9}{\ln 2}W\left({10}^{\frac{1}{4}}\times \frac{\ln 2}{9}\right)=\frac{9}{\ln 2}\times 0.121311=1.575133\end{array}$$

Commented by Tawa11 last updated on 29/Aug/21

$$\mathrm{Great}\mathrm{sir}$$

Commented by Gbenga last updated on 31/Aug/21

$$greatsir$$

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