Algebra Examples

$4 {(2)}^{x} = 128$

Step 1

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

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

Step 2

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

$2^{2 + x} = 128$

Step 3

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

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

Step 4

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

$2 + x = 7$

Step 5

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

Tap for more steps...

Step 5.1

Subtract $2$ from both sides of the equation.

$x = 7 - 2$

Step 5.2

Subtract $2$ from $7$ .

$x = 5$