Whakaoti i te 5^9-x=625

$$5 ^ { 9 - x } = 625$$

Whakaoti mō x

$$x=5$$

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.

$$5^{-x+9}=625$$

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

$$\log(5^{-x+9})=\log(625)$$

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

$$\left(-x+9\right)\log(5)=\log(625)$$

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

$$-x+9=\frac{\log(625)}{\log(5)}$$

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

$$-x+9=\log_{5}\left(625\right)$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$-x=4-9$$

Whakawehea ngā taha e rua ki te -1.

$$x=-\frac{5}{-1}$$

Whakaoti mō x (complex solution)

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

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