Réitigh 2700=1800e^19h

$$2700 = 1800 e ^ { 19 h }$$

Réitigh do h.

$$h=\frac{\ln(\frac{3}{2})}{19}\approx 0.021340269$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 1800.

$$\frac{2700}{1800}=e^{19h}$$

Laghdaigh an codán \frac{2700}{1800} chuig na téarmaí is ísle trí 900 a bhaint agus a chealú.

$$\frac{3}{2}=e^{19h}$$

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

$$e^{19h}=\frac{3}{2}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{19h})=\log(\frac{3}{2})$$

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

$$19h\log(e)=\log(\frac{3}{2})$$

Roinn an dá thaobh faoi \log(e).

$$19h=\frac{\log(\frac{3}{2})}{\log(e)}$$

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

$$19h=\log_{e}\left(\frac{3}{2}\right)$$

Roinn an dá thaobh faoi 19.

$$h=\frac{\ln(\frac{3}{2})}{19}$$

Réitigh do h. (complex solution)

$$h=\frac{2\pi n_{1}i}{19}+\frac{\ln(\frac{3}{2})}{19}$$

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