Whakaoti i te 12^x=100

$$12 ^ { x } = 100$$

Whakaoti mō x

$$x=2\log_{12}\left(10\right)\approx 1.853256816$$

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.

$$12^{x}=100$$

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

$$\log(12^{x})=\log(100)$$

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

$$x\log(12)=\log(100)$$

Whakawehea ngā taha e rua ki te \log(12).

$$x=\frac{\log(100)}{\log(12)}$$

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

$$x=\log_{12}\left(100\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(12)}+2\log_{12}\left(10\right)$$

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