Algebra Examples

$27^{x} = 9^{x - 3}$

Step 1

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

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

Step 2

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

$3 x = 2 (x - 3)$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (x - 3)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $2$ by $- 3$ .

$3 x = 2 x - 6$

Step 3.2

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

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Step 3.2.1

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

$3 x - 2 x = - 6$

Step 3.2.2

Subtract $2 x$ from $3 x$ .

$x = - 6$