Réitigh 6*e^y=200

$$6 \cdot e ^ { y } = 200$$

Réitigh do y.

$$y=-\ln(\frac{3}{100})\approx 3.506557897$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$6e^{y}=200$$

Roinn an dá thaobh faoi 6.

$$e^{y}=\frac{100}{3}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{y})=\log(\frac{100}{3})$$

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

$$y\log(e)=\log(\frac{100}{3})$$

Roinn an dá thaobh faoi \log(e).

$$y=\frac{\log(\frac{100}{3})}{\log(e)}$$

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

$$y=\log_{e}\left(\frac{100}{3}\right)$$

Réitigh do y. (complex solution)

$$y=-\ln(\frac{3}{100})+2\pi n_{1}i$$

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