Whakaoti i te 3*{485}^frac{x{10}}=4000

$$3 \times { 485 }^{ \frac{ x }{ 10 } } = 4000$$

Whakaoti mō x

$$x=-10\log_{485}\left(\frac{3}{4000}\right)\approx 11.635291256$$

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.

$$3\times 485^{\frac{1}{10}x}=4000$$

Whakawehea ngā taha e rua ki te 3.

$$485^{\frac{1}{10}x}=\frac{4000}{3}$$

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

$$\log(485^{\frac{1}{10}x})=\log(\frac{4000}{3})$$

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

$$\frac{1}{10}x\log(485)=\log(\frac{4000}{3})$$

Whakawehea ngā taha e rua ki te \log(485).

$$\frac{1}{10}x=\frac{\log(\frac{4000}{3})}{\log(485)}$$

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

$$\frac{1}{10}x=\log_{485}\left(\frac{4000}{3}\right)$$

Me whakarea ngā taha e rua ki te 10.

$$x=\frac{\ln(\frac{4000}{3})}{\frac{1}{10}\ln(485)}$$

Whakaoti mō x (complex solution)

$$x=\frac{20\pi n_{1}i}{\ln(485)}-10\log_{485}\left(\frac{3}{4000}\right)$$

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