Solve for x 2(5)^x>10

$2 {(5)}^{x} > 10$

Divide each term in $(2 \cdot 5^{x}) > 10$ by $2$ and simplify.

Divide each term in $(2 \cdot 5^{x}) > 10$ by $2$ .

$\frac{(2 \cdot 5^{x})}{2} > \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 5^{x}}{2} > \frac{10}{2}$

Divide $5^{x}$ by $1$ .

$5^{x} > \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$5^{x} > 5$

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

$5^{x} > 5^{1}$

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

$x > 1$

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$