Solve for w 4^(3w+7)=16^11

$4^{3 w + 7} = 16^{11}$

Step 1

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

$4^{3 w + 7} = 4^{2 \cdot 11}$

Step 2

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

$3 w + 7 = 2 \cdot 11$

Step 3

Solve for $w$ .

Multiply $2$ by $11$ .

$3 w + 7 = 22$

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

Subtract $7$ from both sides of the equation.

$3 w = 22 - 7$

Subtract $7$ from $22$ .

$3 w = 15$

Divide each term in $3 w = 15$ by $3$ and simplify.

Divide each term in $3 w = 15$ by $3$ .

$\frac{3 w}{3} = \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 w}{3} = \frac{15}{3}$

Divide $w$ by $1$ .

$w = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$w = 5$