Whakaoti i te 2400/1200=(109/100)^x

$$\frac { 2400 } { 1200 } = ( \frac { 109 } { 100 } ) ^ { x }$$

Whakaoti mō x

$$x=\log_{\frac{109}{100}}\left(2\right)\approx 8.043231727$$

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

Whakawehea te 2400 ki te 1200, kia riro ko 2.

$$2=\left(\frac{109}{100}\right)^{x}$$

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

$$\left(\frac{109}{100}\right)^{x}=2$$

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

$$\log(\left(\frac{109}{100}\right)^{x})=\log(2)$$

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

$$x\log(\frac{109}{100})=\log(2)$$

Whakawehea ngā taha e rua ki te \log(\frac{109}{100}).

$$x=\frac{\log(2)}{\log(\frac{109}{100})}$$

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

$$x=\log_{\frac{109}{100}}\left(2\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{109}{100})}+\log_{\frac{109}{100}}\left(2\right)$$

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