Réitigh (110)^n=1/3855

$$( 110 ) ^ { n } = \frac { 1 } { 3855 }$$

Réitigh do n.

$$n=-\log_{110}\left(3855\right)\approx -1.75665584$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$110^{n}=\frac{1}{3855}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(110^{n})=\log(\frac{1}{3855})$$

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

$$n\log(110)=\log(\frac{1}{3855})$$

Roinn an dá thaobh faoi \log(110).

$$n=\frac{\log(\frac{1}{3855})}{\log(110)}$$

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

$$n=\log_{110}\left(\frac{1}{3855}\right)$$

Réitigh do n. (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(110)}-\log_{110}\left(3855\right)$$

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