Whakaoti i te 9(16)^2x=589824

$$9 ( 16 ) ^ { 2 x } = 589824$$

Whakaoti mō x

$$x=2$$

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.

$$9\times 16^{2x}=589824$$

Whakawehea ngā taha e rua ki te 9.

$$16^{2x}=65536$$

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

$$\log(16^{2x})=\log(65536)$$

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

$$2x\log(16)=\log(65536)$$

Whakawehea ngā taha e rua ki te \log(16).

$$2x=\frac{\log(65536)}{\log(16)}$$

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

$$2x=\log_{16}\left(65536\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{4}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(2)}+2$$

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