Whakaoti i te (500)^x+1=(500)^-5

$$( 500 ) ^ { x + 1 } = ( 500 ) ^ { - 5 }$$

Whakaoti mō x

$$x=-6$$

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.

$$500^{x+1}=\frac{1}{31250000000000}$$

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

$$\log(500^{x+1})=\log(\frac{1}{31250000000000})$$

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

$$\left(x+1\right)\log(500)=\log(\frac{1}{31250000000000})$$

Whakawehea ngā taha e rua ki te \log(500).

$$x+1=\frac{\log(\frac{1}{31250000000000})}{\log(500)}$$

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

$$x+1=\log_{500}\left(\frac{1}{31250000000000}\right)$$

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

$$x=-5-1$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(500)}-6$$

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