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Question Number 183825 by Michaelfaraday last updated on 30/Dec/22

$$solveforxbyusinglambertfunction$$$$2^x+3x=8$$

Answered by MJS_new last updated on 30/Dec/22

$$\mathrm{generally}$$$$b^x=ax+c$$$$\mathrm{inserting}x=-\frac{t}{\ln b}-\frac{c}{a}\mathrm{and}\mathrm{transforming}\mathrm{leads}\mathrm{to}$$$${\mathrm{e}}^{t}t=-\frac{\ln b}{b^{c/a}a}$$$$\Rightarrow x=-\frac{c}{a}-\frac{1}{\ln b}W(-\frac{\ln b}{b^{c/a}a})$$

Commented by Michaelfaraday last updated on 30/Dec/22

$$thankssir$$

Commented by MJS_new last updated on 31/Dec/22

$${\mathrm{you}}^{\prime }\mathrm{re}\mathrm{welcome}$$

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