Réitigh 8000=5000(1005){(e)^12x}

$$8000=5000(1005) {(e)^{ 12x }}$$

Réitigh do x.

$$x=\frac{\ln(2)}{4}-\frac{\ln(5025)}{12}\approx -0.536894933$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Méadaigh 5000 agus 1005 chun 5025000 a fháil.

$$8000=5025000e^{12x}$$

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

$$5025000e^{12x}=8000$$

Roinn an dá thaobh faoi 5025000.

$$e^{12x}=\frac{8000}{5025000}$$

Laghdaigh an codán \frac{8000}{5025000} chuig na téarmaí is ísle trí 1000 a bhaint agus a chealú.

$$e^{12x}=\frac{8}{5025}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{12x})=\log(\frac{8}{5025})$$

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

$$12x\log(e)=\log(\frac{8}{5025})$$

Roinn an dá thaobh faoi \log(e).

$$12x=\frac{\log(\frac{8}{5025})}{\log(e)}$$

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

$$12x=\log_{e}\left(\frac{8}{5025}\right)$$

Roinn an dá thaobh faoi 12.

$$x=\frac{\ln(\frac{8}{5025})}{12}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{6}+\frac{\ln(2)}{4}-\frac{\ln(5025)}{12}$$

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