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Question Number 35491 by mondodotto@gmail.com last updated on 19/May/18

$$\mathbf{prove}\mathbf{that}$$$$3^{\mathit{x}}=9\mathit{x}$$

Commented by math khazana by abdo last updated on 12/Jun/18

$$thequestionisnotcorrectitsonlyaequation$$$$becausey=9xisequationofaliney=3^x=e^{xln\left(3\right)}$$$$neverbeaequationofaline!$$

Answered by candre last updated on 19/May/18

$$x=0\Rightarrow 3^x=1\ne 0=9x$$$$\mathrm{therefore}\mathrm{afirmation}\mathrm{is}\mathrm{false}$$

Commented by Rasheed.Sindhi last updated on 19/May/18

$$\mathrm{This}\mathrm{is}\mathrm{a}\mathrm{conditional}\mathrm{equation}.\mathrm{Therfore}$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{satisfied}\mathrm{by}\mathrm{specific}\mathrm{value}/\mathrm{s}.$$

Commented by candre last updated on 20/May/18

$$\mathrm{but}\mathrm{if}\mathrm{it}\mathrm{was}\mathrm{that}\mathrm{would}\mathrm{it}\mathrm{be}$$$$‘‘\mathrm{find}x\mathrm{such}\mathrm{afirmation}\mathrm{is}{\mathrm{true}}^{″}?$$

Commented by Rasheed.Sindhi last updated on 20/May/18

$$\mathrm{Sir}\mathrm{you}\mathrm{are}\mathrm{right},\mathrm{the}\mathrm{questioner}$$$$\mathrm{has}\mathrm{written}‘‘\mathrm{Prove}{\mathrm{that}}^{″}.\mathrm{I}{\mathrm{didn}}^{\prime }\mathrm{t}$$$$\mathrm{consider}\mathrm{it}\mathrm{at}\mathrm{first}.$$

Answered by rahul 19 last updated on 20/May/18

$$3^3=9\times 3$$$$\Rightarrow x=3.$$

Answered by MrW3 last updated on 12/Jun/18

$$3^x=9x$$$$e^{x\ln 3}=9x$$$$9{xe}^{-x\ln 3}=1$$$$(-x\ln 3)e^{-x\ln 3}=-\frac{\ln 3}{9}$$$$\Rightarrow -x\ln 3=W(-\frac{\ln 3}{9})$$$$\Rightarrow x=-\frac{W(-\frac{\ln 3}{9})}{\ln 3}=\{\begin{array}{l}0.1279\\ 3\end{array}$$

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