Whakaoti i te 9^x=243

$$9 ^ { x } = 243$$

Whakaoti mō x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

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.

$$9^{x}=243$$

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

$$\log(9^{x})=\log(243)$$

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

$$x\log(9)=\log(243)$$

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

$$x=\frac{\log(243)}{\log(9)}$$

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

$$x=\log_{9}\left(243\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+\frac{5}{2}$$

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