Réitigh 1.12^n=2

$$1.12 ^ { n } = 2$$

Réitigh do n.

$$n=\log_{1.12}\left(2\right)\approx 6.116255374$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$1.12^{n}=2$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1.12^{n})=\log(2)$$

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

$$n\log(1.12)=\log(2)$$

Roinn an dá thaobh faoi \log(1.12).

$$n=\frac{\log(2)}{\log(1.12)}$$

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

$$n=\log_{1.12}\left(2\right)$$

Réitigh do n. (complex solution)

$$n=\frac{i\times 2\pi n_{1}}{\ln(1.12)}+\log_{1.12}\left(2\right)$$

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