Whakaoti i te 5*27^x=10.935

$$5 \times 27 ^ { x } = 10.935$$

Whakaoti mō x

$$x=-\log_{3}\left(10\right)+\frac{7}{3}\approx 0.237430059$$

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.

$$5\times 27^{x}=10.935$$

Whakawehea ngā taha e rua ki te 5.

$$27^{x}=2.187$$

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

$$\log(27^{x})=\log(2.187)$$

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

$$x\log(27)=\log(2.187)$$

Whakawehea ngā taha e rua ki te \log(27).

$$x=\frac{\log(2.187)}{\log(27)}$$

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

$$x=\log_{27}\left(2.187\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(3)}-\log_{3}\left(10\right)+\frac{7}{3}$$

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