Finite Math Examples

$\ln (m + 8) - \ln (m) = \ln (3)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{m + 8}{m}) = \ln (3)$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$\frac{m + 8}{m} = 3$

Step 3

Solve for $m$ .

Tap for more steps...

Step 3.1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 3.1.1

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

$m, 1$

Step 3.1.2

The LCM of one and any expression is the expression.

$m$

Step 3.2

Multiply each term in $\frac{m + 8}{m} = 3$ by $m$ to eliminate the fractions.

Tap for more steps...

Step 3.2.1

Multiply each term in $\frac{m + 8}{m} = 3$ by $m$ .

$\frac{m + 8}{m} m = 3 m$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $m$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{m + 8}{m} m = 3 m$

Step 3.2.2.1.2

Rewrite the expression.

$m + 8 = 3 m$

Step 3.3

Solve the equation.

Tap for more steps...

Step 3.3.1

Move all terms containing $m$ to the left side of the equation.

Tap for more steps...

Step 3.3.1.1

Subtract $3 m$ from both sides of the equation.

$m + 8 - 3 m = 0$

Step 3.3.1.2

Subtract $3 m$ from $m$ .

$- 2 m + 8 = 0$

Step 3.3.2

Subtract $8$ from both sides of the equation.

$- 2 m = - 8$

Step 3.3.3

Divide each term in $- 2 m = - 8$ by $- 2$ and simplify.

Tap for more steps...

Step 3.3.3.1

Divide each term in $- 2 m = - 8$ by $- 2$ .

$\frac{- 2 m}{- 2} = \frac{- 8}{- 2}$

Step 3.3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.3.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 2 m}{- 2} = \frac{- 8}{- 2}$

Step 3.3.3.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 8}{- 2}$

Step 3.3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.3.1

Divide $- 8$ by $- 2$ .

$m = 4$