Whakaoti i te 3^x+2=3^5

$$3 ^ { x + 2 } = 3 ^ { 5 }$$

Whakaoti mō x

$$x=3$$

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.

$$3^{x+2}=243$$

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

$$\log(3^{x+2})=\log(243)$$

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

$$\left(x+2\right)\log(3)=\log(243)$$

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

$$x+2=\frac{\log(243)}{\log(3)}$$

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

$$x+2=\log_{3}\left(243\right)$$

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

$$x=5-2$$

Whakaoti mō x (complex solution)

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

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