Solve for x 2^3*4^x=2^11

$2^{3} \cdot 4^{x} = 2^{11}$

Step 1

Rewrite $4$ as $2^{2}$ .

$2^{3} \cdot {(2^{2})}^{x} = 2^{11}$

Step 2

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

$2^{3} \cdot 2^{2 x} = 2^{11}$

Step 3

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

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

Step 4

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

$3 + 2 x = 11$

Step 5

Solve for $x$ .

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

Subtract $3$ from both sides of the equation.

$2 x = 11 - 3$

Subtract $3$ from $11$ .

$2 x = 8$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$