Solve for x 2(8^x)=128

$2 (8^{x}) = 128$

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

$2 \cdot {(2^{3})}^{x} = 128$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 2^{3 x} = 128$

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

$2^{1 + 3 x} = 128$

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

$2^{1 + 3 x} = 2^{7}$

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

$1 + 3 x = 7$

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$3 x = 7 - 1$

Subtract $1$ from $7$ .

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$