Réitigh 1/5e^6x=4

$$\frac { 1 } { 5 } e ^ { 6 x } = 4$$

Réitigh do x.

$$x=\frac{\ln(20)}{6}\approx 0.499288712$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$\frac{1}{5}e^{6x}=4$$

Iolraigh an dá thaobh faoi 5.

$$e^{6x}=20$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{6x})=\log(20)$$

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

$$6x\log(e)=\log(20)$$

Roinn an dá thaobh faoi \log(e).

$$6x=\frac{\log(20)}{\log(e)}$$

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

$$6x=\log_{e}\left(20\right)$$

Roinn an dá thaobh faoi 6.

$$x=\frac{\ln(20)}{6}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{3}+\frac{\ln(20)}{6}$$

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