Whakaoti i te 15^3x-4=10

$$15 ^ { 3 x - 4 } = 10$$

Whakaoti mō x

$$x = \frac{\log_{15} {(506250)}}{3} \approx 1.616758051$$

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.

$$15^{3x-4}=10$$

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

$$\log(15^{3x-4})=\log(10)$$

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

$$\left(3x-4\right)\log(15)=\log(10)$$

Whakawehea ngā taha e rua ki te \log(15).

$$3x-4=\frac{\log(10)}{\log(15)}$$

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

$$3x-4=\log_{15}\left(10\right)$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$3x=\log_{15}\left(10\right)-\left(-4\right)$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{\log_{15}\left(10\right)+4}{3}$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(15)}+\frac{\log_{15}\left(506250\right)}{3}$$

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