Whakaoti i te 3^2x-3=9

$$3 ^ { 2 x - 3 } = 9$$

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.

$$3^{2x-3}=9$$

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

$$\log(3^{2x-3})=\log(9)$$

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

$$\left(2x-3\right)\log(3)=\log(9)$$

Whakawehea ngā taha e rua ki te \log(3).

$$2x-3=\frac{\log(9)}{\log(3)}$$

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

$$2x-3=\log_{3}\left(9\right)$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$2x=2-\left(-3\right)$$

Whakawehea ngā taha e rua ki te 2.

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

Whakaoti mō x (complex solution)

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

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