Solve for x 81^(3x)=27^(x+2)

$81^{3 x} = 27^{x + 2}$

Step 1

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

$3^{4 (3 x)} = 3^{3 (x + 2)}$

Step 2

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

$4 (3 x) = 3 (x + 2)$

Step 3

Solve for $x$ .

Multiply $3$ by $4$ .

$12 x = 3 (x + 2)$

Simplify $3 (x + 2)$ .

Apply the distributive property.

$12 x = 3 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$12 x = 3 x + 6$

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

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

$12 x - 3 x = 6$

Subtract $3 x$ from $12 x$ .

$9 x = 6$

Divide each term in $9 x = 6$ by $9$ and simplify.

Divide each term in $9 x = 6$ by $9$ .

$\frac{9 x}{9} = \frac{6}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{6}{9}$

Divide $x$ by $1$ .

$x = \frac{6}{9}$

Simplify the right side.

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6$ .

$x = \frac{3 (2)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$x = \frac{3 \cdot 2}{3 \cdot 3}$

Cancel the common factor.

$x = \frac{3 \cdot 2}{3 \cdot 3}$

Rewrite the expression.

$x = \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$

Solve for x 81^(3x)=27^(x+2)

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