Whakaoti i te 12^x+3=15

$${ 12 }^{ x+3 } =15$$

Whakaoti mō x

$$x=-\log_{12}\left(\frac{576}{5}\right)\approx -1.910200429$$

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.

$$12^{x+3}=15$$

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

$$\log(12^{x+3})=\log(15)$$

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

$$\left(x+3\right)\log(12)=\log(15)$$

Whakawehea ngā taha e rua ki te \log(12).

$$x+3=\frac{\log(15)}{\log(12)}$$

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

$$x+3=\log_{12}\left(15\right)$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$x=\log_{12}\left(15\right)-3$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(12)}-\log_{12}\left(\frac{576}{5}\right)$$

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