Réitigh 2500=1500(1+.06)^x

$$2500 = 1500 ( 1 + .06 ) ^ { x }$$

Réitigh do x.

$$x=\log_{1.06}\left(\frac{5}{3}\right)\approx 8.766692911$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 1500.

$$\frac{2500}{1500}=\left(1+0.06\right)^{x}$$

Laghdaigh an codán \frac{2500}{1500} chuig na téarmaí is ísle trí 500 a bhaint agus a chealú.

$$\frac{5}{3}=\left(1+0.06\right)^{x}$$

Suimigh 1 agus 0.06 chun 1.06 a fháil.

$$\frac{5}{3}=1.06^{x}$$

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

$$1.06^{x}=\frac{5}{3}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1.06^{x})=\log(\frac{5}{3})$$

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

$$x\log(1.06)=\log(\frac{5}{3})$$

Roinn an dá thaobh faoi \log(1.06).

$$x=\frac{\log(\frac{5}{3})}{\log(1.06)}$$

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

$$x=\log_{1.06}\left(\frac{5}{3}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.06)}+\log_{1.06}\left(\frac{5}{3}\right)$$

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