Whakaoti i te 10(107)^x=2000

$$10 ( 107 ) ^ { x } = 2000$$

Whakaoti mō x

$$x=\log_{107}\left(200\right)\approx 1.133856504$$

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.

$$10\times 107^{x}=2000$$

Whakawehea ngā taha e rua ki te 10.

$$107^{x}=200$$

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

$$\log(107^{x})=\log(200)$$

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

$$x\log(107)=\log(200)$$

Whakawehea ngā taha e rua ki te \log(107).

$$x=\frac{\log(200)}{\log(107)}$$

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

$$x=\log_{107}\left(200\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(107)}+\log_{107}\left(200\right)$$

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