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Question Number 111724 by Aina Samuel Temidayo last updated on 04/Sep/20

$$\mathrm{How}\mathrm{many}\mathrm{real}\mathrm{numbers}\mathrm{x}\mathrm{satisfy}\mathrm{the}$$$$\mathrm{equation}{3}^{2\mathrm{x}+2}-3^{\mathrm{x}+3}-3^{\mathrm{x}}+3=0?$$

Commented by mohammad17 last updated on 05/Sep/20

$$3^{2x}.3^2-3^x.3^3-3^x+3=0$$$$$$$$set:k=3^x$$$$$$$$9k^2-28k+3=0$$$$$$$$k=\frac{-b\mp \sqrt{b^2-4ac}}{2a}\Rightarrow k=\frac{28\mp \sqrt{784-108}}{18}$$$$$$$$k=\frac{28\mp \sqrt{676}}{18}\Rightarrow k=\frac{28\mp 26}{18}$$$$$$$$either:k=\frac{2}{18}\Rightarrow k=\frac{1}{9}\Rightarrow 3^x=\frac{1}{9}\Rightarrow x=\frac{ln\left(\frac{1}{9}\right)}{ln\left(3\right)}\Rightarrow x=-2$$$$$$$$or:k=\frac{54}{18}\Rightarrow k=3\Rightarrow 3^x=3\Rightarrow x=1$$$$$$$$\therefore x=1istrue$$$$$$$$by:\ll mohammad\gg$$

Commented by Aina Samuel Temidayo last updated on 05/Sep/20

$$\mathrm{Thanks}.$$

Commented by Her_Majesty last updated on 05/Sep/20

$$whydoyoucancelx=-2?{it}^{\prime }sarealnumber$$$$and{it}^{\prime }sasolution.$$

Commented by mohammad17 last updated on 05/Sep/20

$$im,sorysirammissed$$

Commented by mohammad17 last updated on 05/Sep/20

$$youarewelcomebutsirx=-2andx=1$$

Commented by Her_Majesty last updated on 05/Sep/20

$$now{it}^{\prime }sright!$$

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