Whakaoti i te 243=9^2x+1

$$243 = 9 ^ { 2 x + 1 }$$

Whakaoti mō x

$$x=\frac{3}{4}=0.75$$

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.

$$9^{2x+1}=243$$

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

$$\log(9^{2x+1})=\log(243)$$

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

$$\left(2x+1\right)\log(9)=\log(243)$$

Whakawehea ngā taha e rua ki te \log(9).

$$2x+1=\frac{\log(243)}{\log(9)}$$

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

$$2x+1=\log_{9}\left(243\right)$$

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

$$2x=\frac{5}{2}-1$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\frac{3}{2}}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{2\ln(3)}+\frac{3}{4}$$

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