Solve for x 8*2^(x+6)=32

$8 \cdot 2^{x + 6} = 32$

Rewrite $8$ as $2^{3}$ .

$2^{3} \cdot 2^{x + 6} = 32$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{3 + x + 6} = 32$

Add $3$ and $6$ .

$2^{x + 9} = 32$

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

$2^{x + 9} = 2^{5}$

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

$x + 9 = 5$

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

Subtract $9$ from both sides of the equation.

$x = 5 - 9$

Subtract $9$ from $5$ .

$x = - 4$