Whakaoti i te e^3m+6=33

$$e ^ { 3 m + 6 } = 33$$

Whakaoti mō m

$$m=\frac{\ln(33)-6}{3}\approx -0.83449748$$

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.

$$e^{3m+6}=33$$

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

$$\log(e^{3m+6})=\log(33)$$

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

$$\left(3m+6\right)\log(e)=\log(33)$$

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

$$3m+6=\frac{\log(33)}{\log(e)}$$

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

$$3m+6=\log_{e}\left(33\right)$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$3m=\ln(33)-6$$

Whakawehea ngā taha e rua ki te 3.

$$m=\frac{\ln(33)-6}{3}$$

Whakaoti mō m (complex solution)

$$m=\frac{i\times 2\pi n_{1}}{3}+\frac{\ln(33)-6}{3}$$

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