Solve for x 4^x-2=0

$4^{x} - 2 = 0$

Step 1

Add $2$ to both sides of the equation.

$4^{x} = 2$

Step 2

Create equivalent expressions in the equation that all have equal bases.

$2^{2 x} = 2^{1}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 x = 1$

Step 4

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$