Réitigh 25^3k=629

$$25 ^ { 3 k } = 629$$

Réitigh do k.

$$k=\frac{\log_{5}\left(629\right)}{6}\approx 0.667327312$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$25^{3k}=629$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(25^{3k})=\log(629)$$

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

$$3k\log(25)=\log(629)$$

Roinn an dá thaobh faoi \log(25).

$$3k=\frac{\log(629)}{\log(25)}$$

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

$$3k=\log_{25}\left(629\right)$$

Roinn an dá thaobh faoi 3.

$$k=\frac{\log_{5}\left(629\right)}{2\times 3}$$

Réitigh do k. (complex solution)

$$k=\frac{\pi n_{1}i}{3\ln(5)}+\frac{\log_{5}\left(629\right)}{6}$$

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