Whakaoti i te (16)^2x=589824

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

Whakaoti mō x

$$x = \frac{\log_{2} {(3)} + 8}{4} \approx 2.396240625$$

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.

$$16^{2x}=589824$$

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

$$\log(16^{2x})=\log(589824)$$

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

$$2x\log(16)=\log(589824)$$

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

$$2x=\frac{\log(589824)}{\log(16)}$$

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

$$2x=\log_{16}\left(589824\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\log_{2}\left(768\right)}{2\times 2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(2)}+\frac{\log_{2}\left(3\right)}{4}+2$$

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