Réitigh 2=1065^n

$$2 = 1065 ^ { n }$$

Réitigh do n.

$$n=\log_{1065}\left(2\right)\approx 0.099436813$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$1065^{n}=2$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1065^{n})=\log(2)$$

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

$$n\log(1065)=\log(2)$$

Roinn an dá thaobh faoi \log(1065).

$$n=\frac{\log(2)}{\log(1065)}$$

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

$$n=\log_{1065}\left(2\right)$$

Réitigh do n. (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(1065)}+\log_{1065}\left(2\right)$$

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