Whakaoti i te 5^2x-3+5^2=26

$${ 5 }^{ 2x-3 } + { 5 }^{ 2 } =26$$

Whakaoti mō x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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.

$$5^{2x-3}+25=26$$

Me tango 25 mai i ngā taha e rua o te whārite.

$$5^{2x-3}=1$$

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

$$\log(5^{2x-3})=\log(1)$$

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

$$\left(2x-3\right)\log(5)=\log(1)$$

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

$$2x-3=\frac{\log(1)}{\log(5)}$$

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

$$2x-3=\log_{5}\left(1\right)$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$2x=-\left(-3\right)$$

Whakawehea ngā taha e rua ki te 2.

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

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(5)}+\frac{3}{2}$$

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