Réitigh 20000=7000{(e)^20x}

$$20000=7000 {(e)^{ 20x }}$$

Réitigh do x.

$$x=\frac{\ln(\frac{20}{7})}{20}\approx 0.052491106$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 7000.

$$\frac{20000}{7000}=e^{20x}$$

Laghdaigh an codán \frac{20000}{7000} chuig na téarmaí is ísle trí 1000 a bhaint agus a chealú.

$$\frac{20}{7}=e^{20x}$$

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

$$e^{20x}=\frac{20}{7}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{20x})=\log(\frac{20}{7})$$

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

$$20x\log(e)=\log(\frac{20}{7})$$

Roinn an dá thaobh faoi \log(e).

$$20x=\frac{\log(\frac{20}{7})}{\log(e)}$$

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

$$20x=\log_{e}\left(\frac{20}{7}\right)$$

Roinn an dá thaobh faoi 20.

$$x=\frac{\ln(\frac{20}{7})}{20}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{10}+\frac{\ln(\frac{20}{7})}{20}$$

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