Solve the Inequality for x 4^x>2^x

$4^{x} > 2^{x}$

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

$2^{2 x} > 2^{x}$

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

$2 x > x$

Move all terms containing $x$ to the left side of the inequality.

Subtract $x$ from both sides of the inequality.

$2 x - x > 0$

Subtract $x$ from $2 x$ .

$x > 0$

The result can be shown in multiple forms.

Inequality Form:

$x > 0$

Interval Notation:

$(0, \infty)$