Réitigh e^frac{x{4}}=20.5

$$e ^ { \frac { x } { 4 } } = 20.5$$

Réitigh do x.

$$x=\ln(176610.0625)\approx 12.081699545$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$e^{\frac{1}{4}x}=20.5$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{\frac{1}{4}x})=\log(20.5)$$

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

$$\frac{1}{4}x\log(e)=\log(20.5)$$

Roinn an dá thaobh faoi \log(e).

$$\frac{1}{4}x=\frac{\log(20.5)}{\log(e)}$$

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

$$\frac{1}{4}x=\log_{e}\left(20.5\right)$$

Iolraigh an dá thaobh faoi 4.

$$x=\frac{\ln(\frac{41}{2})}{\frac{1}{4}}$$

Réitigh do x. (complex solution)

$$x=\ln(176610.0625)+i\times 8\pi n_{1}$$

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