Réitigh 3^n-1=131/8

$${ 3 }^{ n-1 } = 13 \frac{ 1 }{ 8 }$$

Réitigh do n.

$$n=\log_{3}\left(\frac{35}{8}\right)+2\approx 3.343428009$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$3^{n-1}=\frac{105}{8}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(3^{n-1})=\log(\frac{105}{8})$$

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

$$\left(n-1\right)\log(3)=\log(\frac{105}{8})$$

Roinn an dá thaobh faoi \log(3).

$$n-1=\frac{\log(\frac{105}{8})}{\log(3)}$$

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

$$n-1=\log_{3}\left(\frac{105}{8}\right)$$

Cuir 1 leis an dá thaobh den chothromóid.

$$n=\frac{\ln(\frac{105}{8})}{\ln(3)}-\left(-1\right)$$