Réitigh 71=910(0.895)^3x

$$71 = 910 ( 0.895 ) ^ { 3 x }$$

Réitigh do x.

$$x = \frac{\log_{\frac{200}{179}} {(\frac{910}{71})}}{3} \approx 7.664679935$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 910.

$$\frac{71}{910}=0.895^{3x}$$

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

$$0.895^{3x}=\frac{71}{910}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(0.895^{3x})=\log(\frac{71}{910})$$

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

$$3x\log(0.895)=\log(\frac{71}{910})$$

Roinn an dá thaobh faoi \log(0.895).

$$3x=\frac{\log(\frac{71}{910})}{\log(0.895)}$$

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

$$3x=\log_{0.895}\left(\frac{71}{910}\right)$$

Roinn an dá thaobh faoi 3.

$$x=\frac{\ln(\frac{71}{910})}{3\ln(\frac{179}{200})}$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(0.895)}+\frac{\log_{0.895}\left(\frac{71}{910}\right)}{3}$$

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