Réitigh 5^F=20

$$5 ^ { F } = 20$$

Réitigh do F.

$$F=\log_{5}\left(20\right)\approx 1.861353116$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$5^{F}=20$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(5^{F})=\log(20)$$

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

$$F\log(5)=\log(20)$$

Roinn an dá thaobh faoi \log(5).

$$F=\frac{\log(20)}{\log(5)}$$

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

$$F=\log_{5}\left(20\right)$$

Réitigh do F. (complex solution)

$$F=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(20\right)$$

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