Whakaoti i te 4500*137^x=80000

$$4500 \times { 137 }^{ x } =80000$$

Whakaoti mō x

$$x=\log_{137}\left(\frac{160}{9}\right)\approx 0.5849513$$

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.

$$4500\times 137^{x}=80000$$

Whakawehea ngā taha e rua ki te 4500.

$$137^{x}=\frac{160}{9}$$

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

$$\log(137^{x})=\log(\frac{160}{9})$$

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

$$x\log(137)=\log(\frac{160}{9})$$

Whakawehea ngā taha e rua ki te \log(137).

$$x=\frac{\log(\frac{160}{9})}{\log(137)}$$

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

$$x=\log_{137}\left(\frac{160}{9}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(137)}+\log_{137}\left(\frac{160}{9}\right)$$

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