Whakaoti i te 3(6)^2x-3=648

$$3 ( 6 ) ^ { 2 x - 3 } = 648$$

Whakaoti mō x

$$x=3$$

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.

$$3\times 6^{2x-3}=648$$

Whakawehea ngā taha e rua ki te 3.

$$6^{2x-3}=216$$

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

$$\log(6^{2x-3})=\log(216)$$

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

$$\left(2x-3\right)\log(6)=\log(216)$$

Whakawehea ngā taha e rua ki te \log(6).

$$2x-3=\frac{\log(216)}{\log(6)}$$

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

$$2x-3=\log_{6}\left(216\right)$$

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

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

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{6}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(6)}+3$$

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