Whakaoti i te 32^3x-2-48=0

$$32 ^ { 3 x - 2 } - 48 = 0$$

Whakaoti mō x

$$x = \frac{\log_{2} {(3)} + 14}{15} \approx 1.0389975$$

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.

$$32^{3x-2}-48=0$$

Me tāpiri 48 ki ngā taha e rua o te whārite.

$$32^{3x-2}=48$$

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

$$\log(32^{3x-2})=\log(48)$$

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

$$\left(3x-2\right)\log(32)=\log(48)$$

Whakawehea ngā taha e rua ki te \log(32).

$$3x-2=\frac{\log(48)}{\log(32)}$$

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

$$3x-2=\log_{32}\left(48\right)$$

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

$$3x=\frac{\log_{2}\left(48\right)}{5}-\left(-2\right)$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{\frac{\log_{2}\left(48\right)}{5}+2}{3}$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{15\ln(2)}+\frac{\log_{2}\left(3\right)}{15}+\frac{14}{15}$$

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