Solve for x 27^(5x)=9^(x+3)

$27^{5 x} = 9^{x + 3}$

Step 1

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

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

Step 2

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

$3 (5 x) = 2 (x + 3)$

Step 3

Solve for $x$ .

Multiply $5$ by $3$ .

$15 x = 2 (x + 3)$

Simplify $2 (x + 3)$ .

Apply the distributive property.

$15 x = 2 x + 2 \cdot 3$

Multiply $2$ by $3$ .

$15 x = 2 x + 6$

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

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

$15 x - 2 x = 6$

Subtract $2 x$ from $15 x$ .

$13 x = 6$

Divide each term in $13 x = 6$ by $13$ and simplify.

Divide each term in $13 x = 6$ by $13$ .

$\frac{13 x}{13} = \frac{6}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{6}{13}$

Divide $x$ by $1$ .

$x = \frac{6}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{13}$

Decimal Form:

$x = 0.\overline{461538}$