Solve for x 25^x<125^(x-3)

$25^{x} < 125^{x - 3}$

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

$5^{2 x} < 5^{3 (x - 3)}$

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

$2 x < 3 (x - 3)$

Solve for $x$ .

Simplify $3 (x - 3)$ .

Apply the distributive property.

$2 x < 3 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$2 x < 3 x - 9$

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

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

$2 x - 3 x < - 9$

Subtract $3 x$ from $2 x$ .

$- x < - 9$

Divide each term in $- x < - 9$ by $- 1$ and simplify.

Divide each term in $- x < - 9$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 9}{- 1}$

Divide $x$ by $1$ .

$x > \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$x > 9$

The result can be shown in multiple forms.

Inequality Form:

$x > 9$

Interval Notation:

$(9, \infty)$

Solve for x 25^x<125^(x-3)

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