Réitigh 61=3490(0.915)^x-2-109

$$61 = 3490 ( 0.915 ) ^ { x - 2 } - 109$$

Réitigh do x.

$$x=-\log_{0.915}\left(\frac{13960000}{569313}\right)\approx 36.017981429$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$3490\times 0.915^{x-2}-109=61$$

Cuir 109 leis an dá thaobh den chothromóid.

$$3490\times 0.915^{x-2}=170$$

Roinn an dá thaobh faoi 3490.

$$0.915^{x-2}=\frac{17}{349}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(0.915^{x-2})=\log(\frac{17}{349})$$

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

$$\left(x-2\right)\log(0.915)=\log(\frac{17}{349})$$

Roinn an dá thaobh faoi \log(0.915).

$$x-2=\frac{\log(\frac{17}{349})}{\log(0.915)}$$

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

$$x-2=\log_{0.915}\left(\frac{17}{349}\right)$$

Cuir 2 leis an dá thaobh den chothromóid.

$$x=\frac{\ln(\frac{17}{349})}{\ln(\frac{183}{200})}-\left(-2\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.915)}-\log_{0.915}\left(\frac{13960000}{569313}\right)$$

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