Whakaoti i te 49^x-2=343

$$49 ^ { x - 2 } = 343$$

Whakaoti mō x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

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.

$$49^{x-2}=343$$

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

$$\log(49^{x-2})=\log(343)$$

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

$$\left(x-2\right)\log(49)=\log(343)$$

Whakawehea ngā taha e rua ki te \log(49).

$$x-2=\frac{\log(343)}{\log(49)}$$

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

$$x-2=\log_{49}\left(343\right)$$

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

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

Whakaoti mō x (complex solution)

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

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