Whakaoti i te 3^-7x-2=0

$${ 3 }^{ -7x } -2=0$$

Whakaoti mō x

$$x=-\frac{\log_{3}\left(2\right)}{7}\approx -0.090132822$$

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.

$$3^{-7x}-2=0$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$3^{-7x}=2$$

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

$$\log(3^{-7x})=\log(2)$$

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

$$-7x\log(3)=\log(2)$$

Whakawehea ngā taha e rua ki te \log(3).

$$-7x=\frac{\log(2)}{\log(3)}$$

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

$$-7x=\log_{3}\left(2\right)$$

Whakawehea ngā taha e rua ki te -7.

$$x=\frac{\log_{3}\left(2\right)}{-7}$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\pi n_{1}i}{7\ln(3)}-\frac{\log_{3}\left(2\right)}{7}$$

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