Whakaoti i te 700=135{(e)^-0.00866x}

$$700=135 {(e)^{ -0.00866x }}$$

Whakaoti mō x

$$x=\frac{150000\ln(3)-50000\ln(140)}{433}\approx -190.046831017$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakawehea ngā taha e rua ki te 135.

$$\frac{700}{135}=e^{-0.00866x}$$

Whakahekea te hautanga \frac{700}{135} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{140}{27}=e^{-0.00866x}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$e^{-0.00866x}=\frac{140}{27}$$

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

$$\log(e^{-0.00866x})=\log(\frac{140}{27})$$

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

$$-0.00866x\log(e)=\log(\frac{140}{27})$$

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

$$-0.00866x=\frac{\log(\frac{140}{27})}{\log(e)}$$

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

$$-0.00866x=\log_{e}\left(\frac{140}{27}\right)$$

Whakawehea ngā taha e rua o te whārite ki te -0.00866, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=\frac{\ln(\frac{140}{27})}{-0.00866}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 100000\pi n_{1}}{433}+\frac{150000\ln(3)}{433}-\frac{50000\ln(140)}{433}$$

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