Whakaoti i te 9^x+2=6

$$9 ^ { x + 2 } = 6$$

Whakaoti mō x

$$x=\frac{\log_{3}\left(6\right)-4}{2}\approx -1.184535123$$

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.

$$9^{x+2}=6$$

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

$$\log(9^{x+2})=\log(6)$$

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

$$\left(x+2\right)\log(9)=\log(6)$$

Whakawehea ngā taha e rua ki te \log(9).

$$x+2=\frac{\log(6)}{\log(9)}$$

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

$$x+2=\log_{9}\left(6\right)$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x=\frac{\log_{3}\left(6\right)}{2}-2$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+\frac{\log_{3}\left(2\right)}{2}-\frac{3}{2}$$

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