Whakaoti i te 11e^24x=7.5

$$11 { e }^{ 24x } =7.5$$

Whakaoti mō x

$$x=\frac{\ln(\frac{15}{22})}{24}\approx -0.015958011$$

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.

$$11e^{24x}=7.5$$

Whakawehea ngā taha e rua ki te 11.

$$e^{24x}=\frac{15}{22}$$

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

$$\log(e^{24x})=\log(\frac{15}{22})$$

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

$$24x\log(e)=\log(\frac{15}{22})$$

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

$$24x=\frac{\log(\frac{15}{22})}{\log(e)}$$

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

$$24x=\log_{e}\left(\frac{15}{22}\right)$$

Whakawehea ngā taha e rua ki te 24.

$$x=\frac{\ln(\frac{15}{22})}{24}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{12}+\frac{\ln(\frac{15}{22})}{24}$$

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