Whakaoti i te 2=3^x+1

$$2= { 3 }^{ x+1 }$$

Whakaoti mō x

$$x=\log_{3}\left(2\right)-1\approx -0.369070246$$

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.

$$3^{x+1}=2$$

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

$$\log(3^{x+1})=\log(2)$$

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

$$\left(x+1\right)\log(3)=\log(2)$$

Whakawehea ngā taha e rua ki te \log(3).

$$x+1=\frac{\log(2)}{\log(3)}$$

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

$$x+1=\log_{3}\left(2\right)$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=\log_{3}\left(2\right)-1$$

Whakaoti mō x (complex solution)

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

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