Whakaoti i te 3(5^3x+1)=36

$$3 ( 5 ^ { 3 x + 1 } ) = 36$$

Whakaoti mō x

$$x=\frac{\log_{5}\left(12\right)-1}{3}\approx 0.18131977$$

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.

$$3\times 5^{3x+1}=36$$

Whakawehea ngā taha e rua ki te 3.

$$5^{3x+1}=12$$

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

$$\log(5^{3x+1})=\log(12)$$

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

$$\left(3x+1\right)\log(5)=\log(12)$$

Whakawehea ngā taha e rua ki te \log(5).

$$3x+1=\frac{\log(12)}{\log(5)}$$

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

$$3x+1=\log_{5}\left(12\right)$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$3x=\log_{5}\left(12\right)-1$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{\log_{5}\left(12\right)-1}{3}$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(5)}+\frac{\log_{5}\left(12\right)}{3}-\frac{1}{3}$$

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