Whakaoti i te 100000000=67*1026^x

$$100000000 = 67 \times { 1026 }^{ x }$$

Whakaoti mō x

$$x=\log_{1026}\left(\frac{100000000}{67}\right)\approx 2.050356378$$

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

Whakawehea ngā taha e rua ki te 67.

$$\frac{100000000}{67}=1026^{x}$$

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

$$1026^{x}=\frac{100000000}{67}$$

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

$$\log(1026^{x})=\log(\frac{100000000}{67})$$

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

$$x\log(1026)=\log(\frac{100000000}{67})$$

Whakawehea ngā taha e rua ki te \log(1026).

$$x=\frac{\log(\frac{100000000}{67})}{\log(1026)}$$

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

$$x=\log_{1026}\left(\frac{100000000}{67}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1026)}+\log_{1026}\left(\frac{100000000}{67}\right)$$

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