Whakaoti i te 4*3^x+3^x=15

$$4 \cdot 3 ^ { x } + 3 ^ { x } = 15$$

Whakaoti mō x

$$x=1$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Pahekotia te 4\times 3^{x} me 3^{x}, ka 5\times 3^{x}.

$$5\times 3^{x}=15$$

Whakawehea ngā taha e rua ki te 5.

$$3^{x}=\frac{15}{5}$$

Whakawehea te 15 ki te 5, kia riro ko 3.

$$3^{x}=3$$

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

$$\log(3^{x})=\log(3)$$

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

$$x\log(3)=\log(3)$$

Whakawehea ngā taha e rua ki te \log(3).

$$x=\frac{\log(3)}{\log(3)}$$

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

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

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+1$$

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