Whakaoti i te 7^x+6=49

$$7 ^ { x + 6 } = 49$$

Whakaoti mō x

$$x=-4$$

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.

$$7^{x+6}=49$$

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

$$\log(7^{x+6})=\log(49)$$

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

$$\left(x+6\right)\log(7)=\log(49)$$

Whakawehea ngā taha e rua ki te \log(7).

$$x+6=\frac{\log(49)}{\log(7)}$$

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

$$x+6=\log_{7}\left(49\right)$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$x=2-6$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(7)}-4$$

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