Algebra Examples

$125^{c} = 25^{c - 4}$

Step 1

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

$5^{3 c} = 5^{2 (c - 4)}$

Step 2

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

$3 c = 2 (c - 4)$

Step 3

Solve for $c$ .

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Step 3.1

Simplify $2 (c - 4)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $2$ by $- 4$ .

$3 c = 2 c - 8$

Step 3.2

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

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Step 3.2.1

Subtract $2 c$ from both sides of the equation.

$3 c - 2 c = - 8$

Step 3.2.2

Subtract $2 c$ from $3 c$ .

$c = - 8$