Whakaoti i te 3^alpha-5*3+6=0

$$3 ^ { \alpha } - 5 \times 3 + 6 = 0$$

Whakaoti mō α

$$\alpha =2$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakaraupapatia anō ngā kīanga tau.

$$-5\times 3+3^{\alpha }+6=0$$

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$3^{\alpha }-9=0$$

Me tāpiri 9 ki ngā taha e rua o te whārite.

$$3^{\alpha }=9$$

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

$$\log(3^{\alpha })=\log(9)$$

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

$$\alpha \log(3)=\log(9)$$

Whakawehea ngā taha e rua ki te \log(3).

$$\alpha =\frac{\log(9)}{\log(3)}$$

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

$$\alpha =\log_{3}\left(9\right)$$

Whakaoti mō α (complex solution)

$$\alpha =\frac{2\pi n_{1}i}{\ln(3)}+2$$

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