Algebra Examples

$2^{x} \cdot \frac{1}{32} = 32$

Step 1

Subtract $32$ from both sides of the equation.

$2^{x} \cdot \frac{1}{32} - 32 = 0$

Step 2

Combine $2^{x}$ and $\frac{1}{32}$ .

$\frac{2^{x}}{32} - 32 = 0$

Step 3

To write $- 32$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$\frac{2^{x}}{32} - 32 \cdot \frac{32}{32} = 0$

Step 4

Combine $- 32$ and $\frac{32}{32}$ .

$\frac{2^{x}}{32} + \frac{- 32 \cdot 32}{32} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{2^{x} - 32 \cdot 32}{32} = 0$

Step 6

Multiply $- 32$ by $32$ .

$\frac{2^{x} - 1024}{32} = 0$

Step 7

Set the numerator equal to zero.

$2^{x} - 1024 = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Add $1024$ to both sides of the equation.

$2^{x} = 1024$

Step 8.2

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

$2^{x} = 2^{10}$

Step 8.3

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

$x = 10$