Whakaoti i te 5^x2-5x+6=1

$${ 5 }^{ x2-5x+6 } =1$$

Whakaoti mō x

$$x=\frac{x_{2}+6}{5}$$

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.

$$5^{-5x+x_{2}+6}=1$$

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

$$\log(5^{-5x+x_{2}+6})=\log(1)$$

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

$$\left(-5x+x_{2}+6\right)\log(5)=\log(1)$$

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

$$-5x+x_{2}+6=\frac{\log(1)}{\log(5)}$$

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

$$-5x+x_{2}+6=\log_{5}\left(1\right)$$

Me tango x_{2}+6 mai i ngā taha e rua o te whārite.

$$-5x=-\left(x_{2}+6\right)$$

Whakawehea ngā taha e rua ki te -5.

$$x=-\frac{x_{2}+6}{-5}$$

Whakaoti mō x_2

$$x_{2}=5x-6$$

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.

$$5^{x_{2}+6-5x}=1$$

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

$$\log(5^{x_{2}+6-5x})=\log(1)$$

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

$$\left(x_{2}+6-5x\right)\log(5)=\log(1)$$

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

$$x_{2}+6-5x=\frac{\log(1)}{\log(5)}$$

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

$$x_{2}+6-5x=\log_{5}\left(1\right)$$

Me tango -5x+6 mai i ngā taha e rua o te whārite.

$$x_{2}=-\left(6-5x\right)$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\pi n_{1}i}{5\ln(5)}+\frac{x_{2}}{5}+\frac{6}{5}$$

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

Whakaoti mō x_2 (complex solution)

$$x_{2}=\frac{2\pi n_{1}i}{\ln(5)}+5x-6$$

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