Whakaoti i te 7^5x=32

$$7 ^ { 5 x } = 32$$

Whakaoti mō x

$$x=\log_{7}\left(2\right)\approx 0.356207187$$

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.

$$7^{5x}=32$$

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

$$\log(7^{5x})=\log(32)$$

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

$$5x\log(7)=\log(32)$$

Whakawehea ngā taha e rua ki te \log(7).

$$5x=\frac{\log(32)}{\log(7)}$$

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

$$5x=\log_{7}\left(32\right)$$

Whakawehea ngā taha e rua ki te 5.

$$x=\frac{5\log_{7}\left(2\right)}{5}$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(7)}+\log_{7}\left(2\right)$$

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