Whakaoti i te 4845=123^x

$$4845 = { 123 }^{ x }$$

Whakaoti mō x

$$x=\log_{123}\left(4845\right)\approx 1.76337852$$

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

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

$$123^{x}=4845$$

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

$$\log(123^{x})=\log(4845)$$

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

$$x\log(123)=\log(4845)$$

Whakawehea ngā taha e rua ki te \log(123).

$$x=\frac{\log(4845)}{\log(123)}$$

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

$$x=\log_{123}\left(4845\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(4845\right)$$

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