Réitigh 6*2^frac{x{4}}=222

$$6 \cdot 2 ^ { \frac { x } { 4 } } = 222$$

Réitigh do x.

$$x=4\log_{2}\left(37\right)\approx 20.837813463$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$6\times 2^{\frac{1}{4}x}=222$$

Roinn an dá thaobh faoi 6.

$$2^{\frac{1}{4}x}=37$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{\frac{1}{4}x})=\log(37)$$

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

$$\frac{1}{4}x\log(2)=\log(37)$$

Roinn an dá thaobh faoi \log(2).

$$\frac{1}{4}x=\frac{\log(37)}{\log(2)}$$

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

$$\frac{1}{4}x=\log_{2}\left(37\right)$$

Iolraigh an dá thaobh faoi 4.

$$x=\frac{\log_{2}\left(37\right)}{\frac{1}{4}}$$

Réitigh do x. (complex solution)

$$x=\frac{8\pi n_{1}i}{\ln(2)}+4\log_{2}\left(37\right)$$

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