Réitigh 250000*106^x=297754

$$250000 \times { 106 }^{ x } = 297754$$

Réitigh do x.

$$x=3\log_{106}\left(\frac{53}{50}\right)\approx 0.037484509$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$250000\times 106^{x}=297754$$

Roinn an dá thaobh faoi 250000.

$$106^{x}=\frac{148877}{125000}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(106^{x})=\log(\frac{148877}{125000})$$

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

$$x\log(106)=\log(\frac{148877}{125000})$$

Roinn an dá thaobh faoi \log(106).

$$x=\frac{\log(\frac{148877}{125000})}{\log(106)}$$

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

$$x=\log_{106}\left(\frac{148877}{125000}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(106)}+\log_{106}\left(\frac{148877}{125000}\right)$$

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