Réitigh 3*{485}^frac{x{10}}=4000

$$3 \times { 485 }^{ \frac{ x }{ 10 } } = 4000$$

Réitigh do x.

$$x=-10\log_{485}\left(\frac{3}{4000}\right)\approx 11.635291256$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$3\times 485^{\frac{1}{10}x}=4000$$

Roinn an dá thaobh faoi 3.

$$485^{\frac{1}{10}x}=\frac{4000}{3}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(485^{\frac{1}{10}x})=\log(\frac{4000}{3})$$

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

$$\frac{1}{10}x\log(485)=\log(\frac{4000}{3})$$

Roinn an dá thaobh faoi \log(485).

$$\frac{1}{10}x=\frac{\log(\frac{4000}{3})}{\log(485)}$$

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

$$\frac{1}{10}x=\log_{485}\left(\frac{4000}{3}\right)$$

Iolraigh an dá thaobh faoi 10.

$$x=\frac{\ln(\frac{4000}{3})}{\frac{1}{10}\ln(485)}$$

Réitigh do x. (complex solution)

$$x=\frac{20\pi n_{1}i}{\ln(485)}-10\log_{485}\left(\frac{3}{4000}\right)$$

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