Whakaoti i te f(x)=200*116^x=1000

$$f ( x ) = 200 \cdot 116 ^ { x } = 1000$$

Whakaoti mō x

$$x=\log_{116}\left(5\right)\approx 0.338573131$$

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.

$$200\times 116^{x}=1000$$

Whakawehea ngā taha e rua ki te 200.

$$116^{x}=5$$

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

$$\log(116^{x})=\log(5)$$

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

$$x\log(116)=\log(5)$$

Whakawehea ngā taha e rua ki te \log(116).

$$x=\frac{\log(5)}{\log(116)}$$

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

$$x=\log_{116}\left(5\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(116)}+\log_{116}\left(5\right)$$

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