Whakaoti i te 1.08^x=2

$$1.08 ^ { x } = 2$$

Whakaoti mō x

$$x=\log_{1.08}\left(2\right)\approx 9.006468342$$

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.

$$1.08^{x}=2$$

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

$$\log(1.08^{x})=\log(2)$$

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

$$x\log(1.08)=\log(2)$$

Whakawehea ngā taha e rua ki te \log(1.08).

$$x=\frac{\log(2)}{\log(1.08)}$$

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

$$x=\log_{1.08}\left(2\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.08)}+\log_{1.08}\left(2\right)$$

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