Whakaoti i te 4^3x-3=64

$$4 ^ { 3 x - 3 } = 64$$

Whakaoti mō x

$$x=2$$

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.

$$4^{3x-3}=64$$

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

$$\log(4^{3x-3})=\log(64)$$

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

$$\left(3x-3\right)\log(4)=\log(64)$$

Whakawehea ngā taha e rua ki te \log(4).

$$3x-3=\frac{\log(64)}{\log(4)}$$

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

$$3x-3=\log_{4}\left(64\right)$$

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

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

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{6}{3}$$

Whakaoti mō x (complex solution)

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

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