Precalculus Examples

$0 = \log_{3} (2 x + 1) - 3$

Step 1

Rewrite the equation as $\log_{3} (2 x + 1) - 3 = 0$ .

$\log_{3} (2 x + 1) - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$\log_{3} (2 x + 1) = 3$

Step 3

Rewrite $\log_{3} (2 x + 1) = 3$ 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 $b^{y} = x$ .

$3^{3} = 2 x + 1$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $2 x + 1 = 3^{3}$ .

$2 x + 1 = 3^{3}$

Step 4.2

Raise $3$ to the power of $3$ .

$2 x + 1 = 27$

Step 4.3

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

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Step 4.3.1

Subtract $1$ from both sides of the equation.

$2 x = 27 - 1$

Step 4.3.2

Subtract $1$ from $27$ .

$2 x = 26$

Step 4.4

Divide each term in $2 x = 26$ by $2$ and simplify.

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Step 4.4.1

Divide each term in $2 x = 26$ by $2$ .

$\frac{2 x}{2} = \frac{26}{2}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $2$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{26}{2}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{26}{2}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide $26$ by $2$ .

$x = 13$