Whakaoti i te 2.3^2x+1=54

$$2.3 ^ { 2 x + 1 } = 54$$

Whakaoti mō x

$$x=-\frac{\log_{2.3}\left(\frac{23}{540}\right)}{2}\approx 1.89460941$$

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

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$2.3^{2x+1}=54$$

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

$$\log(2.3^{2x+1})=\log(54)$$

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

$$\left(2x+1\right)\log(2.3)=\log(54)$$

Whakawehea ngā taha e rua ki te \log(2.3).

$$2x+1=\frac{\log(54)}{\log(2.3)}$$

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

$$2x+1=\log_{2.3}\left(54\right)$$

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

$$2x=\frac{\ln(54)}{\ln(\frac{23}{10})}-1$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\frac{\ln(54)}{\ln(\frac{23}{10})}-1}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(2.3)}-\frac{\log_{2.3}\left(\frac{23}{540}\right)}{2}$$

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