Whakaoti i te 23^2x=18

$$23 ^ { 2 x } = 18$$

Whakaoti mō x

$$x=\frac{\log_{23}\left(18\right)}{2}\approx 0.460911671$$

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.

$$23^{2x}=18$$

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

$$\log(23^{2x})=\log(18)$$

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

$$2x\log(23)=\log(18)$$

Whakawehea ngā taha e rua ki te \log(23).

$$2x=\frac{\log(18)}{\log(23)}$$

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

$$2x=\log_{23}\left(18\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\log_{23}\left(18\right)}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(23)}+\frac{\log_{23}\left(18\right)}{2}$$

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