Whakaoti i te 100*2^4x=15

$$100 \cdot 2 ^ { 4 x } = 15$$

Whakaoti mō x

$$x=\frac{\log_{2}\left(\frac{3}{5}\right)}{4}-\frac{1}{2}\approx -0.684241399$$

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.

$$100\times 2^{4x}=15$$

Whakawehea ngā taha e rua ki te 100.

$$2^{4x}=\frac{3}{20}$$

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

$$\log(2^{4x})=\log(\frac{3}{20})$$

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

$$4x\log(2)=\log(\frac{3}{20})$$

Whakawehea ngā taha e rua ki te \log(2).

$$4x=\frac{\log(\frac{3}{20})}{\log(2)}$$

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

$$4x=\log_{2}\left(\frac{3}{20}\right)$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{\ln(\frac{3}{20})}{4\ln(2)}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(2)}+\frac{\log_{2}\left(\frac{3}{20}\right)}{4}$$

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