Whakaoti i te 6^22x-3=1

$${ 6 }^{ 22x-3 } =1$$

Whakaoti mō x

$$x=\frac{3}{22}\approx 0.136363636$$

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.

$$6^{22x-3}=1$$

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

$$\log(6^{22x-3})=\log(1)$$

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

$$\left(22x-3\right)\log(6)=\log(1)$$

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

$$22x-3=\frac{\log(1)}{\log(6)}$$

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

$$22x-3=\log_{6}\left(1\right)$$

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

$$22x=-\left(-3\right)$$

Whakawehea ngā taha e rua ki te 22.

$$x=\frac{3}{22}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{11\ln(6)}+\frac{3}{22}$$

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