Solve for x 4^(5x-2)>4^(3x)

$4^{5 x - 2} > 4^{3 x}$

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

$4^{5 x - 2} > 4^{3 x}$

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

$5 x - 2 > 3 x$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the inequality.

$5 x - 2 - 3 x > 0$

Subtract $3 x$ from $5 x$ .

$2 x - 2 > 0$

Add $2$ to both sides of the inequality.

$2 x > 2$

Divide each term in $2 x > 2$ by $2$ and simplify.

Divide each term in $2 x > 2$ by $2$ .

$\frac{2 x}{2} > \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{2}{2}$

Divide $x$ by $1$ .

$x > \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x > 1$

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$