Whakaoti i te 6^x-1=1296

$$6 ^ { x - 1 } = 1296$$

Whakaoti mō x

$$x=5$$

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.

$$6^{x-1}=1296$$

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

$$\log(6^{x-1})=\log(1296)$$

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

$$\left(x-1\right)\log(6)=\log(1296)$$

Whakawehea ngā taha e rua ki te \log(6).

$$x-1=\frac{\log(1296)}{\log(6)}$$

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

$$x-1=\log_{6}\left(1296\right)$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=4-\left(-1\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(6)}+5$$

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