Réitigh 1066.667=1.097^x

$$1066.667 = 1.097 ^ { x }$$

Réitigh do x.

$$x=\log_{1.097}\left(1066.667\right)\approx 75.311684714$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$1.097^{x}=1066.667$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1.097^{x})=\log(1066.667)$$

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

$$x\log(1.097)=\log(1066.667)$$

Roinn an dá thaobh faoi \log(1.097).

$$x=\frac{\log(1066.667)}{\log(1.097)}$$

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

$$x=\log_{1.097}\left(1066.667\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.097)}+\log_{1.097}\left(1066.667\right)$$

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