Whakaoti i te 9^x-1=27

$$9 ^ { x - 1 } = 27$$

Whakaoti mō x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

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.

$$9^{x-1}=27$$

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

$$\log(9^{x-1})=\log(27)$$

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

$$\left(x-1\right)\log(9)=\log(27)$$

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

$$x-1=\frac{\log(27)}{\log(9)}$$

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

$$x-1=\log_{9}\left(27\right)$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\frac{3}{2}-\left(-1\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(3)}+\frac{5}{2}$$

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