Whakaoti i te 61=3490(0.915)^x-2-109

$$61 = 3490 ( 0.915 ) ^ { x - 2 } - 109$$

Whakaoti mō x

$$x=-\log_{0.915}\left(\frac{13960000}{569313}\right)\approx 36.017981429$$

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.

$$3490\times 0.915^{x-2}-109=61$$

Me tāpiri 109 ki ngā taha e rua o te whārite.

$$3490\times 0.915^{x-2}=170$$

Whakawehea ngā taha e rua ki te 3490.

$$0.915^{x-2}=\frac{17}{349}$$

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

$$\log(0.915^{x-2})=\log(\frac{17}{349})$$

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

$$\left(x-2\right)\log(0.915)=\log(\frac{17}{349})$$

Whakawehea ngā taha e rua ki te \log(0.915).

$$x-2=\frac{\log(\frac{17}{349})}{\log(0.915)}$$

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

$$x-2=\log_{0.915}\left(\frac{17}{349}\right)$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=\frac{\ln(\frac{17}{349})}{\ln(\frac{183}{200})}-\left(-2\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.915)}-\log_{0.915}\left(\frac{13960000}{569313}\right)$$

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