Whakaoti i te 102*(102^x-1)=11*002

$$102 \times ( { 102 }^{ x } -1)=11 \times 002$$

Whakaoti mō x

$$x=0$$

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

Whakamahia te āhuatanga tohatoha hei whakarea te 102 ki te 102^{x}-1.

$$102\times 102^{x}-102=11\times 0\times 0\times 2$$

Whakareatia te 11 ki te 0, ka 0.

$$102\times 102^{x}-102=0\times 0\times 2$$

Whakareatia te 0 ki te 0, ka 0.

$$102\times 102^{x}-102=0\times 2$$

Whakareatia te 0 ki te 2, ka 0.

$$102\times 102^{x}-102=0$$

Me tāpiri 102 ki ngā taha e rua o te whārite.

$$102\times 102^{x}=102$$

Whakawehea ngā taha e rua ki te 102.

$$102^{x}=1$$

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

$$\log(102^{x})=\log(1)$$

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

$$x\log(102)=\log(1)$$

Whakawehea ngā taha e rua ki te \log(102).

$$x=\frac{\log(1)}{\log(102)}$$

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

$$x=\log_{102}\left(1\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(102)}$$

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