Whakaoti i te 12^x-9-7=23

$${ 12 }^{ x-9 } -7 = 23$$

Whakaoti mō x

$$x=\log_{12}\left(154793410560\right)\approx 10.368742517$$

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

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$12^{x-9}-7=23$$

Me tāpiri 7 ki ngā taha e rua o te whārite.

$$12^{x-9}=30$$

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

$$\log(12^{x-9})=\log(30)$$

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

$$\left(x-9\right)\log(12)=\log(30)$$

Whakawehea ngā taha e rua ki te \log(12).

$$x-9=\frac{\log(30)}{\log(12)}$$

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

$$x-9=\log_{12}\left(30\right)$$

Me tāpiri 9 ki ngā taha e rua o te whārite.

$$x=\log_{12}\left(30\right)-\left(-9\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(12)}+\log_{12}\left(154793410560\right)$$

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