Whakaoti i te 9^23/9^11=9^x

$$\frac { 9 ^ { 23 } } { 9 ^ { 11 } } = 9 ^ { x }$$

Whakaoti mō x

$$x=12$$

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

Hei whakawehe ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga. Me tango te 11 i te 23 kia riro ai te 12.

$$9^{12}=9^{x}$$

Tātaihia te 9 mā te pū o 12, kia riro ko 282429536481.

$$282429536481=9^{x}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$9^{x}=282429536481$$

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

$$\log(9^{x})=\log(282429536481)$$

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

$$x\log(9)=\log(282429536481)$$

Whakawehea ngā taha e rua ki te \log(9).

$$x=\frac{\log(282429536481)}{\log(9)}$$

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

$$x=\log_{9}\left(282429536481\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+12$$

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