Whakaoti i te 132^x=8

$${ 132 }^{ x } =8$$

Whakaoti mō x

$$x=3\log_{132}\left(2\right)\approx 0.42587055$$

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.

$$132^{x}=8$$

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

$$\log(132^{x})=\log(8)$$

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

$$x\log(132)=\log(8)$$

Whakawehea ngā taha e rua ki te \log(132).

$$x=\frac{\log(8)}{\log(132)}$$

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

$$x=\log_{132}\left(8\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(132)}+3\log_{132}\left(2\right)$$

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