Réitigh 1000000=418658*left(10250right)^x

$$1000000=418658 \times { \left(10250 \right) }^{ x }$$

Réitigh do x.

$$x=\log_{10250}\left(\frac{500000}{209329}\right)\approx 0.094282383$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 418658.

$$\frac{1000000}{418658}=10250^{x}$$

Laghdaigh an codán \frac{1000000}{418658} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$\frac{500000}{209329}=10250^{x}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$10250^{x}=\frac{500000}{209329}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(10250^{x})=\log(\frac{500000}{209329})$$

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

$$x\log(10250)=\log(\frac{500000}{209329})$$

Roinn an dá thaobh faoi \log(10250).

$$x=\frac{\log(\frac{500000}{209329})}{\log(10250)}$$

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

$$x=\log_{10250}\left(\frac{500000}{209329}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10250)}+\log_{10250}\left(\frac{500000}{209329}\right)$$

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