Whakaoti i te 5^x+1=15625

$${ 5 }^{ x+1 } =15625$$

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.

$$5^{x+1}=15625$$

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

$$\log(5^{x+1})=\log(15625)$$

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

$$\left(x+1\right)\log(5)=\log(15625)$$

Whakawehea ngā taha e rua ki te \log(5).

$$x+1=\frac{\log(15625)}{\log(5)}$$

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

$$x+1=\log_{5}\left(15625\right)$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=6-1$$

Whakaoti mō x (complex solution)

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

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