Réitigh 12(2^x-5)=500

$$12 ( 2 ^ { x - 5 } ) = 500$$

Réitigh do x.

$$x=\log_{2}\left(\frac{125}{3}\right)+5\approx 10.380821784$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$12\times 2^{x-5}=500$$

Roinn an dá thaobh faoi 12.

$$2^{x-5}=\frac{125}{3}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{x-5})=\log(\frac{125}{3})$$

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

$$\left(x-5\right)\log(2)=\log(\frac{125}{3})$$

Roinn an dá thaobh faoi \log(2).

$$x-5=\frac{\log(\frac{125}{3})}{\log(2)}$$

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

$$x-5=\log_{2}\left(\frac{125}{3}\right)$$

Cuir 5 leis an dá thaobh den chothromóid.

$$x=\frac{\ln(\frac{125}{3})}{\ln(2)}-\left(-5\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(\frac{125}{3}\right)+5$$

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