Precalculus Examples

$2^{x - 3} = 32$

Step 1

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

$2^{x - 3} = 2^{5}$

Step 2

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

$x - 3 = 5$

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

$x = 5 + 3$

Step 3.2

Add $5$ and $3$ .

$x = 8$