Finite Math Examples

$25^{2 x} = 125^{x - 2}$

Step 1

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

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

Step 2

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

$2 (2 x) = 3 (x - 2)$

Step 3

Solve for $x$ .

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Step 3.1

Multiply $2$ by $2$ .

$4 x = 3 (x - 2)$

Step 3.2

Simplify $3 (x - 2)$ .

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Step 3.2.1

Apply the distributive property.

$4 x = 3 x + 3 \cdot - 2$

Step 3.2.2

Multiply $3$ by $- 2$ .

$4 x = 3 x - 6$

Step 3.3

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

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Step 3.3.1

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

$4 x - 3 x = - 6$

Step 3.3.2

Subtract $3 x$ from $4 x$ .

$x = - 6$