Réitigh 1100=104^x

$$1100 = 104 ^ { x }$$

Réitigh do x.

$$x=\log_{104}\left(1100\right)\approx 1.507854444$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$104^{x}=1100$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(104^{x})=\log(1100)$$

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

$$x\log(104)=\log(1100)$$

Roinn an dá thaobh faoi \log(104).

$$x=\frac{\log(1100)}{\log(104)}$$

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

$$x=\log_{104}\left(1100\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(104)}+\log_{104}\left(1100\right)$$

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