Whakaoti i te 9^x-4=81

$$9 ^ { x - 4 } = 81$$

Whakaoti mō x

$$x=6$$

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.

$$9^{x-4}=81$$

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

$$\log(9^{x-4})=\log(81)$$

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

$$\left(x-4\right)\log(9)=\log(81)$$

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

$$x-4=\frac{\log(81)}{\log(9)}$$

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

$$x-4=\log_{9}\left(81\right)$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=2-\left(-4\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(3)}+6$$

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