Finite Math Examples

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

Step 1

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

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

Step 2

Move all terms not containing $\log_{3} (2 x + 1)$ to the right side of the equation.

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Step 2.1

Add $3$ to both sides of the equation.

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

Step 2.2

Add $2$ and $3$ .

$\log_{3} (2 x + 1) = 5$

Step 3

Rewrite $\log_{3} (2 x + 1) = 5$ 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 $b^{y} = x$ .

$3^{5} = 2 x + 1$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $2 x + 1 = 3^{5}$ .

$2 x + 1 = 3^{5}$

Step 4.2

Raise $3$ to the power of $5$ .

$2 x + 1 = 243$

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.

$2 x = 243 - 1$

Step 4.3.2

Subtract $1$ from $243$ .

$2 x = 242$

Step 4.4

Divide each term in $2 x = 242$ by $2$ and simplify.

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Step 4.4.1

Divide each term in $2 x = 242$ by $2$ .

$\frac{2 x}{2} = \frac{242}{2}$

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.

$\frac{2 x}{2} = \frac{242}{2}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{242}{2}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide $242$ by $2$ .

$x = 121$