Réitigh 94*2^frac{x{3}}=16

$$94 \cdot 2 ^ { \frac { x } { 3 } } = 16$$

Réitigh do x.

$$x=-3\log_{2}\left(47\right)+9\approx -7.663766555$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$94\times 2^{\frac{1}{3}x}=16$$

Roinn an dá thaobh faoi 94.

$$2^{\frac{1}{3}x}=\frac{8}{47}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{\frac{1}{3}x})=\log(\frac{8}{47})$$

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

$$\frac{1}{3}x\log(2)=\log(\frac{8}{47})$$

Roinn an dá thaobh faoi \log(2).

$$\frac{1}{3}x=\frac{\log(\frac{8}{47})}{\log(2)}$$

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

$$\frac{1}{3}x=\log_{2}\left(\frac{8}{47}\right)$$

Iolraigh an dá thaobh faoi 3.

$$x=\frac{-\log_{2}\left(47\right)+3}{\frac{1}{3}}$$

Réitigh do x. (complex solution)

$$x=\frac{6\pi n_{1}i}{\ln(2)}-3\log_{2}\left(47\right)+9$$

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