Réitigh 6e^-4x-10-4=63

$$6 e ^ { - 4 x - 10 } - 4 = 63$$

Réitigh do x.

$$x=\frac{\ln(\frac{6}{67})-10}{4}\approx -3.103233288$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Úsáid rialacha na n-easpónant agus na logartam chun an chothromóid a réiteach.

$$6e^{-4x-10}-4=63$$

Cuir 4 leis an dá thaobh den chothromóid.

$$6e^{-4x-10}=67$$

Roinn an dá thaobh faoi 6.

$$e^{-4x-10}=\frac{67}{6}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{-4x-10})=\log(\frac{67}{6})$$

Is ionann logartam uimhreacha a ardaítear go cumhacht agus an chumhacht méadaithe faoi logartam na huimhreach.

$$\left(-4x-10\right)\log(e)=\log(\frac{67}{6})$$

Roinn an dá thaobh faoi \log(e).

$$-4x-10=\frac{\log(\frac{67}{6})}{\log(e)}$$

Leis an bhfoirmle athrú boinn \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$-4x-10=\log_{e}\left(\frac{67}{6}\right)$$

Cuir 10 leis an dá thaobh den chothromóid.

$$-4x=\ln(\frac{67}{6})-\left(-10\right)$$

Roinn an dá thaobh faoi -4.

$$x=\frac{\ln(\frac{67}{6})+10}{-4}$$

Réitigh do x. (complex solution)

$$x=-\frac{\pi n_{1}i}{2}+\frac{\ln(\frac{6}{67})-10}{4}$$

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