Réitigh 47=610(0.5)^frac{x{4}}

$$47 = 610 ( 0.5 ) ^ { \frac { x } { 4 } }$$

Réitigh do x.

$$x=4\log_{2}\left(\frac{610}{47}\right)\approx 14.792306323$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 610.

$$\frac{47}{610}=0.5^{\frac{x}{4}}$$

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

$$0.5^{\frac{x}{4}}=\frac{47}{610}$$

Úsáid rialacha na n-easpónant agus na logartam chun an chothromóid a réiteach.

$$0.5^{\frac{1}{4}x}=\frac{47}{610}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(0.5^{\frac{1}{4}x})=\log(\frac{47}{610})$$

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

$$\frac{1}{4}x\log(0.5)=\log(\frac{47}{610})$$

Roinn an dá thaobh faoi \log(0.5).

$$\frac{1}{4}x=\frac{\log(\frac{47}{610})}{\log(0.5)}$$

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

$$\frac{1}{4}x=\log_{0.5}\left(\frac{47}{610}\right)$$

Iolraigh an dá thaobh faoi 4.

$$x=-\frac{\frac{\ln(\frac{47}{610})}{\ln(2)}}{\frac{1}{4}}$$