Whakaoti i te 108^x=2

$$108 ^ { x } = 2$$

Whakaoti mō x

$$x=\log_{108}\left(2\right)\approx 0.148040955$$

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.

$$108^{x}=2$$

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

$$\log(108^{x})=\log(2)$$

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

$$x\log(108)=\log(2)$$

Whakawehea ngā taha e rua ki te \log(108).

$$x=\frac{\log(2)}{\log(108)}$$

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

$$x=\log_{108}\left(2\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(108)}+\log_{108}\left(2\right)$$

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