Réitigh 3*2^frac{x{5}}=150

$$3 \cdot 2 ^ { \frac { x } { 5 } } = 150$$

Réitigh do x.

$$x=10\log_{2}\left(5\right)+5\approx 28.219280949$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$3\times 2^{\frac{1}{5}x}=150$$

Roinn an dá thaobh faoi 3.

$$2^{\frac{1}{5}x}=50$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{\frac{1}{5}x})=\log(50)$$

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

$$\frac{1}{5}x\log(2)=\log(50)$$

Roinn an dá thaobh faoi \log(2).

$$\frac{1}{5}x=\frac{\log(50)}{\log(2)}$$

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

$$\frac{1}{5}x=\log_{2}\left(50\right)$$

Iolraigh an dá thaobh faoi 5.

$$x=\frac{\log_{2}\left(50\right)}{\frac{1}{5}}$$

Réitigh do x. (complex solution)

$$x=\frac{10\pi n_{1}i}{\ln(2)}+10\log_{2}\left(5\right)+5$$

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