Réitigh 14400=4000(1025)^x

$$14400 = 4000 ( 1025 ) ^ { x }$$

Réitigh do x.

$$x=\log_{1025}\left(\frac{18}{5}\right)\approx 0.184773671$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 4000.

$$\frac{14400}{4000}=1025^{x}$$

Laghdaigh an codán \frac{14400}{4000} chuig na téarmaí is ísle trí 800 a bhaint agus a chealú.

$$\frac{18}{5}=1025^{x}$$

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

$$1025^{x}=\frac{18}{5}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1025^{x})=\log(\frac{18}{5})$$

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

$$x\log(1025)=\log(\frac{18}{5})$$

Roinn an dá thaobh faoi \log(1025).

$$x=\frac{\log(\frac{18}{5})}{\log(1025)}$$

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

$$x=\log_{1025}\left(\frac{18}{5}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1025)}+\log_{1025}\left(\frac{18}{5}\right)$$

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