Whakaoti i te 5^x-2=1

$$5 ^ { x - 2 } = 1$$

Whakaoti mō x

$$x=2$$

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.

$$5^{x-2}=1$$

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

$$\log(5^{x-2})=\log(1)$$

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

$$\left(x-2\right)\log(5)=\log(1)$$

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

$$x-2=\frac{\log(1)}{\log(5)}$$

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

$$x-2=\log_{5}\left(1\right)$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

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

Whakaoti mō x (complex solution)

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

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