Precalculus Examples

$f (x) = \log_{2} (2 x - 5)$

Step 1

Set $\log_{2} (2 x - 5)$ equal to $0$ .

$\log_{2} (2 x - 5) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite $\log_{2} (2 x - 5) = 0$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$2^{0} = 2 x - 5$

Step 2.2

Solve for $x$ .

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Step 2.2.1

Rewrite the equation as $2 x - 5 = 2^{0}$ .

$2 x - 5 = 2^{0}$

Step 2.2.2

Anything raised to $0$ is $1$ .

$2 x - 5 = 1$

Step 2.2.3

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

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Step 2.2.3.1

Add $5$ to both sides of the equation.

$2 x = 1 + 5$

Step 2.2.3.2

Add $1$ and $5$ .

$2 x = 6$

Step 2.2.4

Divide each term in $2 x = 6$ by $2$ and simplify.

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Step 2.2.4.1

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Step 2.2.4.2

Simplify the left side.

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Step 2.2.4.2.1

Cancel the common factor of $2$ .

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Step 2.2.4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Step 2.2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Step 2.2.4.3

Simplify the right side.

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Step 2.2.4.3.1

Divide $6$ by $2$ .

$x = 3$

Step 3