Réitigh 2400/1200=(109/100)^x

$$\frac { 2400 } { 1200 } = ( \frac { 109 } { 100 } ) ^ { x }$$

Réitigh do x.

$$x=\log_{\frac{109}{100}}\left(2\right)\approx 8.043231727$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn 2400 faoi 1200 chun 2 a fháil.

$$2=\left(\frac{109}{100}\right)^{x}$$

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

$$\left(\frac{109}{100}\right)^{x}=2$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(\left(\frac{109}{100}\right)^{x})=\log(2)$$

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

$$x\log(\frac{109}{100})=\log(2)$$

Roinn an dá thaobh faoi \log(\frac{109}{100}).

$$x=\frac{\log(2)}{\log(\frac{109}{100})}$$

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

$$x=\log_{\frac{109}{100}}\left(2\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{109}{100})}+\log_{\frac{109}{100}}\left(2\right)$$

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