Whakaoti i te 3^6x-3=81

$$3 ^ { 6 x - 3 } = 81$$

Whakaoti mō x

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

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.

$$3^{6x-3}=81$$

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

$$\log(3^{6x-3})=\log(81)$$

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

$$\left(6x-3\right)\log(3)=\log(81)$$

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

$$6x-3=\frac{\log(81)}{\log(3)}$$

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

$$6x-3=\log_{3}\left(81\right)$$

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

$$6x=4-\left(-3\right)$$

Whakawehea ngā taha e rua ki te 6.

$$x=\frac{7}{6}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{3\ln(3)}+\frac{7}{6}$$

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