Whakaoti i te 1000000=418658*left(10250right)^x

$$1000000=418658 \times { \left(10250 \right) }^{ x }$$

Whakaoti mō x

$$x=\log_{10250}\left(\frac{500000}{209329}\right)\approx 0.094282383$$

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

Whakawehea ngā taha e rua ki te 418658.

$$\frac{1000000}{418658}=10250^{x}$$

Whakahekea te hautanga \frac{1000000}{418658} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{500000}{209329}=10250^{x}$$

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

$$10250^{x}=\frac{500000}{209329}$$

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

$$\log(10250^{x})=\log(\frac{500000}{209329})$$

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

$$x\log(10250)=\log(\frac{500000}{209329})$$

Whakawehea ngā taha e rua ki te \log(10250).

$$x=\frac{\log(\frac{500000}{209329})}{\log(10250)}$$

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

$$x=\log_{10250}\left(\frac{500000}{209329}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10250)}+\log_{10250}\left(\frac{500000}{209329}\right)$$

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