Réitigh 592*3^2x=74

$$592 \cdot 3 ^ { 2 x } = 74$$

Réitigh do x.

$$x=-\frac{3\log_{3}\left(2\right)}{2}\approx -0.94639463$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$592\times 3^{2x}=74$$

Roinn an dá thaobh faoi 592.

$$3^{2x}=\frac{1}{8}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(3^{2x})=\log(\frac{1}{8})$$

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

$$2x\log(3)=\log(\frac{1}{8})$$

Roinn an dá thaobh faoi \log(3).

$$2x=\frac{\log(\frac{1}{8})}{\log(3)}$$

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

$$2x=\log_{3}\left(\frac{1}{8}\right)$$

Roinn an dá thaobh faoi 2.

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

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}-\frac{3\log_{3}\left(2\right)}{2}$$

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