Solve for x 5*11^(x+3)=55

$5 \cdot 11^{x + 3} = 55$

Divide each term in $(5 \cdot 11^{x + 3}) = 55$ by $5$ and simplify.

Divide each term in $(5 \cdot 11^{x + 3}) = 55$ by $5$ .

$\frac{(5 \cdot 11^{x + 3})}{5} = \frac{55}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 \cdot 11^{x + 3}}{5} = \frac{55}{5}$

Divide $11^{x + 3}$ by $1$ .

$11^{x + 3} = \frac{55}{5}$

Simplify the right side.

Divide $55$ by $5$ .

$11^{x + 3} = 11$

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

$11^{x + 3} = 11^{1}$

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

$x + 3 = 1$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$x = 1 - 3$

Subtract $3$ from $1$ .

$x = - 2$