Whakaoti i te 3(5^2x-1)+14=92

$$3 ( 5 ^ { 2 x - 1 } ) + 14 = 92$$

Whakaoti mō x

$$x = \frac{\log_{5} {(26)} + 1}{2} \approx 1.5121846$$

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.

$$3\times 5^{2x-1}+14=92$$

Me tango 14 mai i ngā taha e rua o te whārite.

$$3\times 5^{2x-1}=78$$

Whakawehea ngā taha e rua ki te 3.

$$5^{2x-1}=26$$

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

$$\log(5^{2x-1})=\log(26)$$

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

$$\left(2x-1\right)\log(5)=\log(26)$$

Whakawehea ngā taha e rua ki te \log(5).

$$2x-1=\frac{\log(26)}{\log(5)}$$

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

$$2x-1=\log_{5}\left(26\right)$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$2x=\log_{5}\left(26\right)-\left(-1\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\log_{5}\left(26\right)+1}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(5)}+\frac{\log_{5}\left(130\right)}{2}$$

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