Precalculus Examples

$f (x) = \log_{2} (2 x - 7)$

Step 1

Set the argument in $\log_{2} (2 x - 7)$ greater than $0$ to find where the expression is defined.

$2 x - 7 > 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $7$ to both sides of the inequality.

$2 x > 7$

Step 2.2

Divide each term in $2 x > 7$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x > 7$ by $2$ .

$\frac{2 x}{2} > \frac{7}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} > \frac{7}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{7}{2}$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(\frac{7}{2}, \infty)$

Set-Builder Notation:

${x | x > \frac{7}{2}}$

Step 4