Precalculus Examples

$\log (2 x + 4) = 1$

Step 1

Rewrite $\log (2 x + 4) = 1$ 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 $b^{y} = x$ .

$10^{1} = 2 x + 4$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $2 x + 4 = 10^{1}$ .

$2 x + 4 = 10$

Step 2.2

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

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Step 2.2.1

Subtract $4$ from both sides of the equation.

$2 x = 10 - 4$

Step 2.2.2

Subtract $4$ from $10$ .

$2 x = 6$

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $x$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $6$ by $2$ .

$x = 3$