Réitigh 27^2x=98

$$27 ^ { 2 x } = 98$$

Réitigh do x.

$$x=\frac{\log_{3}\left(98\right)}{6}\approx 0.695569542$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Úsáid rialacha na n-easpónant agus na logartam chun an chothromóid a réiteach.

$$27^{2x}=98$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(27^{2x})=\log(98)$$

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

$$2x\log(27)=\log(98)$$

Roinn an dá thaobh faoi \log(27).

$$2x=\frac{\log(98)}{\log(27)}$$

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

$$2x=\log_{27}\left(98\right)$$

Roinn an dá thaobh faoi 2.

$$x=\frac{\log_{3}\left(98\right)}{2\times 3}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{3\ln(3)}+\frac{\log_{3}\left(98\right)}{6}$$

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