Finite Math Examples

$\log_{4} (4 x - 6) = 1$

Step 1

Rewrite $\log_{4} (4 x - 6) = 1$ 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 $b^{y} = x$ .

$4^{1} = 4 x - 6$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $4 x - 6 = 4^{1}$ .

$4 x - 6 = 4$

Step 2.2

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

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Step 2.2.1

Add $6$ to both sides of the equation.

$4 x = 4 + 6$

Step 2.2.2

Add $4$ and $6$ .

$4 x = 10$

Step 2.3

Divide each term in $4 x = 10$ by $4$ and simplify.

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Step 2.3.1

Divide each term in $4 x = 10$ by $4$ .

$\frac{4 x}{4} = \frac{10}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{10}{4}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $10$ and $4$ .

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Step 2.3.3.1.1

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{4}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.3.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Step 2.3.3.1.2.3

Rewrite the expression.

$x = \frac{5}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

$x = 2 \frac{1}{2}$