Whakaoti i te 2097=5954.3{(e)^x*(-0.00896)}

$$2097=5954.3 {(e)^{ x \times (-0.00896) }}$$

Whakaoti mō x

$$x=\frac{3125\ln(59543)-3125\ln(20970)}{28}\approx 116.473872288$$

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

Whakawehea ngā taha e rua ki te 5954.3.

$$\frac{2097}{5954.3}=e^{x\left(-0.00896\right)}$$

Whakarohaina te \frac{2097}{5954.3} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\frac{20970}{59543}=e^{x\left(-0.00896\right)}$$

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

$$e^{x\left(-0.00896\right)}=\frac{20970}{59543}$$

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$e^{-0.00896x}=\frac{20970}{59543}$$

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

$$\log(e^{-0.00896x})=\log(\frac{20970}{59543})$$

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

$$-0.00896x\log(e)=\log(\frac{20970}{59543})$$

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

$$-0.00896x=\frac{\log(\frac{20970}{59543})}{\log(e)}$$

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

$$-0.00896x=\log_{e}\left(\frac{20970}{59543}\right)$$

Whakawehea ngā taha e rua o te whārite ki te -0.00896, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=\frac{\ln(\frac{20970}{59543})}{-0.00896}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 3125\pi n_{1}}{14}+\frac{3125\ln(59543)}{28}-\frac{3125\ln(20970)}{28}$$

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