Whakaoti i te 3^x-2*3^x*3^-2=7

$${ 3 }^{ x } -2 \times { 3 }^{ x } \times { 3 }^{ -2 } =7$$

Whakaoti mō x

$$x=2$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Tātaihia te 3 mā te pū o -2, kia riro ko \frac{1}{9}.

$$3^{x}-2\times 3^{x}\times \frac{1}{9}=7$$

Whakareatia te 2 ki te \frac{1}{9}, ka \frac{2}{9}.

$$3^{x}-\frac{2}{9}\times 3^{x}=7$$

Pahekotia te 3^{x} me -\frac{2}{9}\times 3^{x}, ka \frac{7}{9}\times 3^{x}.

$$\frac{7}{9}\times 3^{x}=7$$

Me whakarea ngā taha e rua ki te \frac{9}{7}, te tau utu o \frac{7}{9}.

$$3^{x}=7\times \frac{9}{7}$$

Whakareatia te 7 ki te \frac{9}{7}, ka 9.

$$3^{x}=9$$

Tuhia te tau taupū kōaro o ngā taha e rua o te whārite.

$$\log(3^{x})=\log(9)$$

Ko te taupū kōaro o tētahi tau ka hīkina ki tētahi pū ko te pū whakarea ki te taupū kōaro o taua tau.

$$x\log(3)=\log(9)$$

Whakawehea ngā taha e rua ki te \log(3).

$$x=\frac{\log(9)}{\log(3)}$$

Mā te tikanga tātai huri pūtake \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{3}\left(9\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+2$$

$$n_{1}\in \mathrm{Z}$$