Whakaoti i te (5825)^(x-3)=120

$$( 5825 ) ^ { ( x - 3 ) } = 120$$

Whakaoti mō x

$$x=\log_{5825}\left(23717506875000\right)\approx 3.552195972$$

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.

$$5825^{x-3}=120$$

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

$$\log(5825^{x-3})=\log(120)$$

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

$$\left(x-3\right)\log(5825)=\log(120)$$

Whakawehea ngā taha e rua ki te \log(5825).

$$x-3=\frac{\log(120)}{\log(5825)}$$

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

$$x-3=\log_{5825}\left(120\right)$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=\log_{5825}\left(120\right)-\left(-3\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5825)}+\log_{5825}\left(23717506875000\right)$$

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