Réitigh 450=130{(e)^-71(x)}

$$450=130 {(e)^{ -71(x) }}$$

Réitigh do x.

$$x=\frac{\ln(\frac{13}{45})}{71}\approx -0.017488917$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 130.

$$\frac{450}{130}=e^{-71x}$$

Laghdaigh an codán \frac{450}{130} chuig na téarmaí is ísle trí 10 a bhaint agus a chealú.

$$\frac{45}{13}=e^{-71x}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$e^{-71x}=\frac{45}{13}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{-71x})=\log(\frac{45}{13})$$

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

$$-71x\log(e)=\log(\frac{45}{13})$$

Roinn an dá thaobh faoi \log(e).

$$-71x=\frac{\log(\frac{45}{13})}{\log(e)}$$

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

$$-71x=\log_{e}\left(\frac{45}{13}\right)$$

Roinn an dá thaobh faoi -71.

$$x=\frac{\ln(\frac{45}{13})}{-71}$$

Réitigh do x. (complex solution)

$$x=-\frac{2\pi n_{1}i}{71}+\frac{\ln(\frac{13}{45})}{71}$$

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