Réitigh 2*16^2n=70

$$2 \cdot 16 ^ { 2 n } = 70$$

Réitigh do n.

$$n=\frac{\log_{2}\left(35\right)}{8}\approx 0.641160377$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$2\times 16^{2n}=70$$

Roinn an dá thaobh faoi 2.

$$16^{2n}=35$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(16^{2n})=\log(35)$$

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

$$2n\log(16)=\log(35)$$

Roinn an dá thaobh faoi \log(16).

$$2n=\frac{\log(35)}{\log(16)}$$

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

$$2n=\log_{16}\left(35\right)$$

Roinn an dá thaobh faoi 2.

$$n=\frac{\log_{2}\left(35\right)}{2\times 4}$$

Réitigh do n. (complex solution)

$$n=\frac{\pi n_{1}i}{4\ln(2)}+\frac{\log_{2}\left(35\right)}{8}$$

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