Finite Math Examples

$\frac{x}{x + 4} = - \ln (3)$

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 4, 1$

Step 1.2

Remove parentheses.

$x + 4, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x + 4$

Step 2

Multiply each term in $\frac{x}{x + 4} = - \ln (3)$ by $x + 4$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $\frac{x}{x + 4} = - \ln (3)$ by $x + 4$ .

$\frac{x}{x + 4} (x + 4) = - \ln (3) (x + 4)$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $x + 4$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{x}{x + 4} (x + 4) = - \ln (3) (x + 4)$

Step 2.2.1.2

Rewrite the expression.

$x = - \ln (3) (x + 4)$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

$x = - \ln (3) x - \ln (3) \cdot 4$

Step 2.3.2

Multiply $- \ln (3) \cdot 4$ .

Tap for more steps...

Step 2.3.2.1

Multiply $4$ by $- 1$ .

$x = - \ln (3) x - 4 \ln (3)$

Step 2.3.2.2

Simplify $- 4 \ln (3)$ by moving $4$ inside the logarithm.

$x = - \ln (3) x - \ln (3^{4})$

Step 2.3.3

Raise $3$ to the power of $4$ .

$x = - \ln (3) x - \ln (81)$

Step 2.3.4

Reorder factors in $- \ln (3) x - \ln (81)$ .

$x = - x \ln (3) - \ln (81)$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Move all the terms containing a logarithm to the left side of the equation.

$x \ln (3) + \ln (81) = - x$

Step 3.2

Add $x$ to both sides of the equation.

$x \ln (3) + \ln (81) + x = 0$

Step 3.3

Subtract $\ln (81)$ from both sides of the equation.

$x \ln (3) + x = - \ln (81)$

Step 3.4

Factor $x$ out of $x \ln (3) + x$ .

Tap for more steps...

Step 3.4.1

Factor $x$ out of $x \ln (3)$ .

$x (\ln (3)) + x = - \ln (81)$

Step 3.4.2

Raise $x$ to the power of $1$ .

$x (\ln (3)) + x = - \ln (81)$

Step 3.4.3

Factor $x$ out of $x^{1}$ .

$x (\ln (3)) + x \cdot 1 = - \ln (81)$

Step 3.4.4

Factor $x$ out of $x (\ln (3)) + x \cdot 1$ .

$x (\ln (3) + 1) = - \ln (81)$

Step 3.5

Divide each term in $x (\ln (3) + 1) = - \ln (81)$ by $\ln (3) + 1$ and simplify.

Tap for more steps...

Step 3.5.1

Divide each term in $x (\ln (3) + 1) = - \ln (81)$ by $\ln (3) + 1$ .

$\frac{x (\ln (3) + 1)}{\ln (3) + 1} = \frac{- \ln (81)}{\ln (3) + 1}$

Step 3.5.2

Simplify the left side.

Tap for more steps...

Step 3.5.2.1

Cancel the common factor of $\ln (3) + 1$ .

Tap for more steps...

Step 3.5.2.1.1

Cancel the common factor.

$\frac{x (\ln (3) + 1)}{\ln (3) + 1} = \frac{- \ln (81)}{\ln (3) + 1}$

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \ln (81)}{\ln (3) + 1}$

Step 3.5.3

Simplify the right side.

Tap for more steps...

Step 3.5.3.1

Move the negative in front of the fraction.

$x = - \frac{\ln (81)}{\ln (3) + 1}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\ln (81)}{\ln (3) + 1}$

Decimal Form:

$x = - 2.09397856 \dots$