Whakaoti i te 9^3-x=81

$$9 ^ { 3 - x } = 81$$

Whakaoti mō x

$$x=1$$

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.

$$9^{-x+3}=81$$

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

$$\log(9^{-x+3})=\log(81)$$

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

$$\left(-x+3\right)\log(9)=\log(81)$$

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

$$-x+3=\frac{\log(81)}{\log(9)}$$

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

$$-x+3=\log_{9}\left(81\right)$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$-x=2-3$$

Whakawehea ngā taha e rua ki te -1.

$$x=-\frac{1}{-1}$$

Whakaoti mō x (complex solution)

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

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