Precalculus Examples

$y = 2^{x - 3} - 4$

Step 1

Set $2^{x - 3} - 4$ equal to $0$ .

$2^{x - 3} - 4 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $4$ to both sides of the equation.

$2^{x - 3} = 4$

Step 2.2

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

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

Step 2.3

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

$x - 3 = 2$

Step 2.4

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

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Step 2.4.1

Add $3$ to both sides of the equation.

$x = 2 + 3$

Step 2.4.2

Add $2$ and $3$ .

$x = 5$

Step 3