Solve 02^x+0*525/sqrt{5}=04^x

$$\frac{ 0 { 2 }^{ x+0 \cdot 5 } 25 }{ \sqrt{ 5 } } = 0 { 4 }^{ x }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Multiply 0 and 5 to get 0.

$$\frac{0\times 2^{x+0}\times 25}{\sqrt{5}}=0\times 4^{x}$$

Anything plus zero gives itself.

$$\frac{0\times 2^{x}\times 25}{\sqrt{5}}=0\times 4^{x}$$

Multiply 0 and 25 to get 0.

$$\frac{0\times 2^{x}}{\sqrt{5}}=0\times 4^{x}$$

Rationalize the denominator of \frac{0\times 2^{x}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{0\times 2^{x}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}=0\times 4^{x}$$

The square of \sqrt{5} is 5.

$$\frac{0\times 2^{x}\sqrt{5}}{5}=0\times 4^{x}$$

Divide 0\times 2^{x}\sqrt{5} by 5 to get 0\times 2^{x}\sqrt{5}.

$$0\times 2^{x}\sqrt{5}=0\times 4^{x}$$

Subtract 0\times 4^{x} from both sides.

$$0\times 2^{x}\sqrt{5}-0\times 4^{x}=0$$

Reorder the terms.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply 0 and 5 to get 0.

$$\frac{0\times 2^{x+0}\times 25}{\sqrt{5}}=0\times 4^{x}$$

Anything plus zero gives itself.

$$\frac{0\times 2^{x}\times 25}{\sqrt{5}}=0\times 4^{x}$$

Multiply 0 and 25 to get 0.

$$\frac{0\times 2^{x}}{\sqrt{5}}=0\times 4^{x}$$

Rationalize the denominator of \frac{0\times 2^{x}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{0\times 2^{x}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}=0\times 4^{x}$$

The square of \sqrt{5} is 5.

$$\frac{0\times 2^{x}\sqrt{5}}{5}=0\times 4^{x}$$

Divide 0\times 2^{x}\sqrt{5} by 5 to get 0\times 2^{x}\sqrt{5}.

$$0\times 2^{x}\sqrt{5}=0\times 4^{x}$$

Subtract 0\times 4^{x} from both sides.

$$0\times 2^{x}\sqrt{5}-0\times 4^{x}=0$$

Reorder the terms.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$