Whakaoti i te 5^3x-7=25

$$5 ^ { 3 x - 7 } = 25$$

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.

$$5^{3x-7}=25$$

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

$$\log(5^{3x-7})=\log(25)$$

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

$$\left(3x-7\right)\log(5)=\log(25)$$

Whakawehea ngā taha e rua ki te \log(5).

$$3x-7=\frac{\log(25)}{\log(5)}$$

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

$$3x-7=\log_{5}\left(25\right)$$

Me tāpiri 7 ki ngā taha e rua o te whārite.

$$3x=2-\left(-7\right)$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{9}{3}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(5)}+3$$

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