Whakaoti i te 3^23*3^x*3^19=3^78

$$3 ^ { 23 } \times 3 ^ { x } \times 3 ^ { 19 } = 3 ^ { 78 }$$

Whakaoti mō x

$$x=36$$

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.

$$109418989131512359209\times 3^{x}=16423203268260658146231467800709255289$$

Whakawehea ngā taha e rua ki te 109418989131512359209.

$$3^{x}=150094635296999121$$

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

$$\log(3^{x})=\log(150094635296999121)$$

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

$$x\log(3)=\log(150094635296999121)$$

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

$$x=\frac{\log(150094635296999121)}{\log(3)}$$

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

$$x=\log_{3}\left(150094635296999121\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+36$$

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