Whakaoti i te 6200=990(1115)^x+2900

$$6200 = 990 ( 1115 ) ^ { x } + 2900$$

Whakaoti mō x

$$x=\log_{1115}\left(\frac{10}{3}\right)\approx 0.171588967$$

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.

$$990\times 1115^{x}+2900=6200$$

Me tango 2900 mai i ngā taha e rua o te whārite.

$$990\times 1115^{x}=3300$$

Whakawehea ngā taha e rua ki te 990.

$$1115^{x}=\frac{10}{3}$$

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

$$\log(1115^{x})=\log(\frac{10}{3})$$

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

$$x\log(1115)=\log(\frac{10}{3})$$

Whakawehea ngā taha e rua ki te \log(1115).

$$x=\frac{\log(\frac{10}{3})}{\log(1115)}$$

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

$$x=\log_{1115}\left(\frac{10}{3}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1115)}+\log_{1115}\left(\frac{10}{3}\right)$$

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