Réitigh 11*13^x-14=106

$$11 \times { 13 }^{ x } -14=106$$

Réitigh do x.

$$x=\log_{13}\left(\frac{120}{11}\right)\approx 0.931634951$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$11\times 13^{x}-14=106$$

Cuir 14 leis an dá thaobh den chothromóid.

$$11\times 13^{x}=120$$

Roinn an dá thaobh faoi 11.

$$13^{x}=\frac{120}{11}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(13^{x})=\log(\frac{120}{11})$$

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

$$x\log(13)=\log(\frac{120}{11})$$

Roinn an dá thaobh faoi \log(13).

$$x=\frac{\log(\frac{120}{11})}{\log(13)}$$

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

$$x=\log_{13}\left(\frac{120}{11}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(13)}+\log_{13}\left(\frac{120}{11}\right)$$

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