Whakaoti i te 12(25)^x-1=75

$$12 ( 25 ) ^ { x - 1 } = 75$$

Whakaoti mō x

$$x=-\log_{5}\left(2\right)+2\approx 1.569323442$$

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.

$$12\times 25^{x-1}=75$$

Whakawehea ngā taha e rua ki te 12.

$$25^{x-1}=\frac{25}{4}$$

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

$$\log(25^{x-1})=\log(\frac{25}{4})$$

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

$$\left(x-1\right)\log(25)=\log(\frac{25}{4})$$

Whakawehea ngā taha e rua ki te \log(25).

$$x-1=\frac{\log(\frac{25}{4})}{\log(25)}$$

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

$$x-1=\log_{25}\left(\frac{25}{4}\right)$$

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

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

Whakaoti mō x (complex solution)

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

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