Finite Math Examples

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

Step 1

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

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

Step 2

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

$2 x = 3 (x + 2)$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $3 (x + 2)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $3$ by $2$ .

$2 x = 3 x + 6$

Step 3.2

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

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Step 3.2.1

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

$2 x - 3 x = 6$

Step 3.2.2

Subtract $3 x$ from $2 x$ .

$- x = 6$

Step 3.3

Divide each term in $- x = 6$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- x = 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{6}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{6}{- 1}$

Step 3.3.2.2

Divide $x$ by $1$ .

$x = \frac{6}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $6$ by $- 1$ .

$x = - 6$