Réitigh (1/2)^x=1/32

$$( \frac { 1 } { 2 } ) ^ { x } = \frac { 1 } { 32 }$$

Réitigh do x.

$$x=5$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$\left(\frac{1}{2}\right)^{x}=\frac{1}{32}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(\left(\frac{1}{2}\right)^{x})=\log(\frac{1}{32})$$

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

$$x\log(\frac{1}{2})=\log(\frac{1}{32})$$

Roinn an dá thaobh faoi \log(\frac{1}{2}).

$$x=\frac{\log(\frac{1}{32})}{\log(\frac{1}{2})}$$

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

$$x=\log_{\frac{1}{2}}\left(\frac{1}{32}\right)$$

Réitigh do x. (complex solution)

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

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