Whakaoti i te 1418519125=106^x

$$1418519125= { 106 }^{ x }$$

Whakaoti mō x

$$x=\log_{106}\left(1418519125\right)\approx 4.518742256$$

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.

$$106^{x}=1418519125$$

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

$$\log(106^{x})=\log(1418519125)$$

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

$$x\log(106)=\log(1418519125)$$

Whakawehea ngā taha e rua ki te \log(106).

$$x=\frac{\log(1418519125)}{\log(106)}$$

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

$$x=\log_{106}\left(1418519125\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(106)}+\log_{106}\left(1418519125\right)$$

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