Atrisiniet sqrt2^x=sqrt{2}quada=?

$$\sqrt { 2 } ^ { x } = \sqrt { 2 } \quad a = ?$$

Atrast a

$$a=\frac{2^{\frac{x+1}{2}}}{2}$$

Lineāra vienādojuma risināšanas darbības

Mainiet puses tā, lai visi mainīgie locekļi atrastos pa kreisi.

$$\sqrt{2}a=\left(\sqrt{2}\right)^{x}$$

Daliet abas puses ar \sqrt{2}.

$$\frac{\sqrt{2}a}{\sqrt{2}}=\frac{2^{\frac{x}{2}}}{\sqrt{2}}$$

Dalīšana ar \sqrt{2} atsauc reizināšanu ar \sqrt{2}.

$$a=\frac{2^{\frac{x}{2}}}{\sqrt{2}}$$

Daliet 2^{\frac{x}{2}} ar \sqrt{2}.

$$a=2^{\frac{x-1}{2}}$$

Atrast x (complex solution)

$$x=\frac{2\ln(a)+\ln(2)}{\ln(2)}+\frac{4\pi n_{1}i}{\ln(2)}$$

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

$$a\neq 0$$

Atrast x

$$x=2\log_{2}\left(a\right)+1$$

$$a>0$$