Whakaoti i te 5^x-7=1/125

$$5 ^ { x - 7 } = \frac { 1 } { 125 }$$

Whakaoti mō x

$$x=4$$

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.

$$5^{x-7}=\frac{1}{125}$$

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

$$\log(5^{x-7})=\log(\frac{1}{125})$$

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

$$\left(x-7\right)\log(5)=\log(\frac{1}{125})$$

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

$$x-7=\frac{\log(\frac{1}{125})}{\log(5)}$$

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

$$x-7=\log_{5}\left(\frac{1}{125}\right)$$

Me tāpiri 7 ki ngā taha e rua o te whārite.

$$x=-3-\left(-7\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(5)}+4$$

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