Whakaoti i te 7^7/7^3=7^x

$$\frac { 7 ^ { 7 } } { 7 ^ { 3 } } = 7 ^ { x }$$

Whakaoti mō x

$$x=4$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Hei whakawehe ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga. Me tango te 3 i te 7 kia riro ai te 4.

$$7^{4}=7^{x}$$

Tātaihia te 7 mā te pū o 4, kia riro ko 2401.

$$2401=7^{x}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$7^{x}=2401$$

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

$$\log(7^{x})=\log(2401)$$

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

$$x\log(7)=\log(2401)$$

Whakawehea ngā taha e rua ki te \log(7).

$$x=\frac{\log(2401)}{\log(7)}$$

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

$$x=\log_{7}\left(2401\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+4$$

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