Solve for x 2^(4(x-3))=16^(x+1)

$2^{4 (x - 3)} = 16^{x + 1}$

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

$2^{4 (x - 3)} = 2^{4 (x + 1)}$

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

$4 (x - 3) = 4 (x + 1)$

Solve for $x$ .

Simplify $4 (x - 3)$ .

Start simplifying.

$0 + 0 + 4 (x - 3) = 4 (x + 1)$

Simplify by adding zeros.

$4 (x - 3) = 4 (x + 1)$

Apply the distributive property.

$4 x + 4 \cdot - 3 = 4 (x + 1)$

Multiply $4$ by $- 3$ .

$4 x - 12 = 4 (x + 1)$

Simplify $4 (x + 1)$ .

Apply the distributive property.

$4 x - 12 = 4 x + 4 \cdot 1$

Multiply $4$ by $1$ .

$4 x - 12 = 4 x + 4$

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

Subtract $4 x$ from both sides of the equation.

$4 x - 12 - 4 x = 4$

Combine the opposite terms in $4 x - 12 - 4 x$ .

Subtract $4 x$ from $4 x$ .

$0 - 12 = 4$

Subtract $12$ from $0$ .

$- 12 = 4$

Since $- 12 \neq 4$ , there are no solutions.

No solution