Réitigh 5^-x=4

$$5 ^ { - x } = 4$$

Réitigh do x.

$$x=-2\log_{5}\left(2\right)\approx -0.861353116$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$5^{-x}=4$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(5^{-x})=\log(4)$$

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

$$-x\log(5)=\log(4)$$

Roinn an dá thaobh faoi \log(5).

$$-x=\frac{\log(4)}{\log(5)}$$

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

$$-x=\log_{5}\left(4\right)$$

Roinn an dá thaobh faoi -1.

$$x=\frac{2\log_{5}\left(2\right)}{-1}$$

Réitigh do x. (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(5)}-2\log_{5}\left(2\right)$$

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