Réitigh (1/3)^x=211/560

$$( \frac { 1 } { 3 } ) ^ { x } = \frac { 211 } { 560 }$$

Réitigh do x.

$$x=-\log_{3}\left(\frac{211}{560}\right)\approx 0.888465076$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$\left(\frac{1}{3}\right)^{x}=\frac{211}{560}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(\left(\frac{1}{3}\right)^{x})=\log(\frac{211}{560})$$

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

$$x\log(\frac{1}{3})=\log(\frac{211}{560})$$

Roinn an dá thaobh faoi \log(\frac{1}{3}).

$$x=\frac{\log(\frac{211}{560})}{\log(\frac{1}{3})}$$

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

$$x=\log_{\frac{1}{3}}\left(\frac{211}{560}\right)$$

Réitigh do x. (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(3)}-\log_{3}\left(\frac{211}{560}\right)$$

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