Réitigh 4845=123^x

$$4845 = { 123 }^{ x }$$

Réitigh do x.

$$x=\log_{123}\left(4845\right)\approx 1.76337852$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$123^{x}=4845$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(123^{x})=\log(4845)$$

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

$$x\log(123)=\log(4845)$$

Roinn an dá thaobh faoi \log(123).

$$x=\frac{\log(4845)}{\log(123)}$$

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

$$x=\log_{123}\left(4845\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(4845\right)$$

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