Réitigh 3800=1.23^x

$$3800 = 1.23 ^ { x }$$

Réitigh do x.

$$x=\log_{1.23}\left(3800\right)\approx 39.817353422$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$1.23^{x}=3800$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1.23^{x})=\log(3800)$$

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

$$x\log(1.23)=\log(3800)$$

Roinn an dá thaobh faoi \log(1.23).

$$x=\frac{\log(3800)}{\log(1.23)}$$

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

$$x=\log_{1.23}\left(3800\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.23)}+\log_{1.23}\left(3800\right)$$

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