Réitigh -3*4^-10n=-39

$$- 3 \cdot 4 ^ { - 10 n } = - 39$$

Réitigh do n.

$$n=-\frac{\log_{2}\left(13\right)}{20}\approx -0.185021986$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi -3.

$$4^{-10n}=\frac{-39}{-3}$$

Roinn -39 faoi -3 chun 13 a fháil.

$$4^{-10n}=13$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(4^{-10n})=\log(13)$$

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

$$-10n\log(4)=\log(13)$$

Roinn an dá thaobh faoi \log(4).

$$-10n=\frac{\log(13)}{\log(4)}$$

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

$$-10n=\log_{4}\left(13\right)$$

Roinn an dá thaobh faoi -10.

$$n=\frac{\log_{2}\left(13\right)}{-10\times 2}$$

Réitigh do n. (complex solution)

$$n=-\frac{\pi n_{1}i}{10\ln(2)}-\frac{\log_{2}\left(13\right)}{20}$$

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