Whakaoti i te 12^y-6=3

$$12 ^ { y - 6 } = 3$$

Whakaoti mō y

$$y=\log_{12}\left(8957952\right)\approx 6.442114109$$

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.

$$12^{y-6}=3$$

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

$$\log(12^{y-6})=\log(3)$$

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

$$\left(y-6\right)\log(12)=\log(3)$$

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

$$y-6=\frac{\log(3)}{\log(12)}$$

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

$$y-6=\log_{12}\left(3\right)$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$y=\log_{12}\left(3\right)-\left(-6\right)$$

Whakaoti mō y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(12)}+\log_{12}\left(8957952\right)$$

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