Réitigh e^y-6=8

$$e ^ { y - 6 } = 8$$

Réitigh do y.

$$y=3\left(\ln(2)+2\right)\approx 8.079441542$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$e^{y-6}=8$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{y-6})=\log(8)$$

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

$$\left(y-6\right)\log(e)=\log(8)$$

Roinn an dá thaobh faoi \log(e).

$$y-6=\frac{\log(8)}{\log(e)}$$

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

$$y-6=\log_{e}\left(8\right)$$

Cuir 6 leis an dá thaobh den chothromóid.

$$y=3\ln(2)-\left(-6\right)$$

Réitigh do y. (complex solution)

$$y=3\ln(2)+6+2\pi n_{1}i$$

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