Solve for x 11^(2x+12)-3=118

$11^{2 x + 12} - 3 = 118$

Step 1

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

Add $3$ to both sides of the equation.

$11^{2 x + 12} = 118 + 3$

Add $118$ and $3$ .

$11^{2 x + 12} = 121$

Step 2

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

$11^{2 x + 12} = 11^{2}$

Step 3

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

$2 x + 12 = 2$

Step 4

Solve for $x$ .

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

Subtract $12$ from both sides of the equation.

$2 x = 2 - 12$

Subtract $12$ from $2$ .

$2 x = - 10$

Divide each term in $2 x = - 10$ by $2$ and simplify.

Divide each term in $2 x = - 10$ by $2$ .

$\frac{2 x}{2} = \frac{- 10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 10}{2}$

Divide $x$ by $1$ .

$x = \frac{- 10}{2}$

Simplify the right side.

Divide $- 10$ by $2$ .

$x = - 5$