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

prove that 3^x =9x

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{3}^{\boldsymbol{{x}}} =\mathrm{9}\boldsymbol{{x}} \\ $$

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

the question is not correct its only a equation because y=9x is equation of a line y=3^x =e^(xln(3)) never be a equation of a line !

$${the}\:{question}\:{is}\:{not}\:{correct}\:{its}\:{only}\:{a}\:{equation}\: \\ $$$${because}\:{y}=\mathrm{9}{x}\:{is}\:{equation}\:{of}\:{a}\:{line}\:\:{y}=\mathrm{3}^{{x}} \:={e}^{{xln}\left(\mathrm{3}\right)} \\ $$$${never}\:{be}\:{a}\:{equation}\:{of}\:{a}\:{line}\:! \\ $$

Answered by candre last updated on 19/May/18

x=0⇒3^x =1≠0=9x therefore afirmation is false

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

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

This is a conditional equation.Therfore it′s satisfied by specific value/s.

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

Commented by candre last updated on 20/May/18

but if it was that would it be “find x such afirmation is true”?

$$\mathrm{but}\:\mathrm{if}\:\mathrm{it}\:\mathrm{was}\:\mathrm{that}\:\mathrm{would}\:\mathrm{it}\:\mathrm{be} \\ $$$$``\mathrm{find}\:{x}\:\mathrm{such}\:\mathrm{afirmation}\:\mathrm{is}\:\mathrm{true}''? \\ $$

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

Sir you are right,the questioner has written “Prove that”.I didn′t consider it at first.

$$\mathrm{Sir}\:\mathrm{you}\:\mathrm{are}\:\mathrm{right},\mathrm{the}\:\mathrm{questioner} \\ $$$$\mathrm{has}\:\mathrm{written}\:``\mathrm{Prove}\:\mathrm{that}''.\mathrm{I}\:\mathrm{didn}'\mathrm{t} \\ $$$$\mathrm{consider}\:\mathrm{it}\:\mathrm{at}\:\mathrm{first}. \\ $$

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

3^3 = 9×3 ⇒ x=3.

$$\mathrm{3}^{\mathrm{3}} =\:\mathrm{9}×\mathrm{3} \\ $$$$\Rightarrow\:{x}=\mathrm{3}. \\ $$

Answered by MrW3 last updated on 12/Jun/18

3^x =9x e^(xln 3) =9x 9xe^(−xln 3) =1 (−xln 3)e^(−xln 3) =−((ln 3)/9) ⇒−xln 3=W(−((ln 3)/9)) ⇒x=−((W(−((ln 3)/9)))/(ln 3))= { ((0.1279)),(3) :}

$$\mathrm{3}^{{x}} =\mathrm{9}{x} \\ $$$${e}^{{x}\mathrm{ln}\:\mathrm{3}} =\mathrm{9}{x} \\ $$$$\mathrm{9}{xe}^{−{x}\mathrm{ln}\:\mathrm{3}} =\mathrm{1} \\ $$$$\left(−{x}\mathrm{ln}\:\mathrm{3}\right){e}^{−{x}\mathrm{ln}\:\mathrm{3}} =−\frac{\mathrm{ln}\:\mathrm{3}}{\mathrm{9}} \\ $$$$\Rightarrow−{x}\mathrm{ln}\:\mathrm{3}={W}\left(−\frac{\mathrm{ln}\:\mathrm{3}}{\mathrm{9}}\right) \\ $$$$\Rightarrow{x}=−\frac{{W}\left(−\frac{\mathrm{ln}\:\mathrm{3}}{\mathrm{9}}\right)}{\mathrm{ln}\:\mathrm{3}}=\begin{cases}{\mathrm{0}.\mathrm{1279}}\\{\mathrm{3}}\end{cases} \\ $$

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