Réitigh 100000000=67*1026^x

$$100000000 = 67 \times { 1026 }^{ x }$$

Réitigh do x.

$$x=\log_{1026}\left(\frac{100000000}{67}\right)\approx 2.050356378$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 67.

$$\frac{100000000}{67}=1026^{x}$$

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

$$1026^{x}=\frac{100000000}{67}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1026^{x})=\log(\frac{100000000}{67})$$

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

$$x\log(1026)=\log(\frac{100000000}{67})$$

Roinn an dá thaobh faoi \log(1026).

$$x=\frac{\log(\frac{100000000}{67})}{\log(1026)}$$

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

$$x=\log_{1026}\left(\frac{100000000}{67}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1026)}+\log_{1026}\left(\frac{100000000}{67}\right)$$

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