Finite Math Examples

$\ln (\frac{8 x + 11}{x}) = \ln (9)$

Step 1

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

$\frac{8 x + 11}{x} = 9$

Step 2

Solve for $x$ .

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Step 2.1

Find the LCD of the terms in the equation.

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Step 2.1.1

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

$x, 1$

Step 2.1.2

The LCM of one and any expression is the expression.

$x$

Step 2.2

Multiply each term in $\frac{8 x + 11}{x} = 9$ by $x$ to eliminate the fractions.

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Step 2.2.1

Multiply each term in $\frac{8 x + 11}{x} = 9$ by $x$ .

$\frac{8 x + 11}{x} x = 9 x$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $x$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{8 x + 11}{x} x = 9 x$

Step 2.2.2.1.2

Rewrite the expression.

$8 x + 11 = 9 x$

Step 2.3

Solve the equation.

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Step 2.3.1

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

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Step 2.3.1.1

Subtract $9 x$ from both sides of the equation.

$8 x + 11 - 9 x = 0$

Step 2.3.1.2

Subtract $9 x$ from $8 x$ .

$- x + 11 = 0$

Step 2.3.2

Subtract $11$ from both sides of the equation.

$- x = - 11$

Step 2.3.3

Divide each term in $- x = - 11$ by $- 1$ and simplify.

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Step 2.3.3.1

Divide each term in $- x = - 11$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 11}{- 1}$

Step 2.3.3.2

Simplify the left side.

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Step 2.3.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 11}{- 1}$

Step 2.3.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 11}{- 1}$

Step 2.3.3.3

Simplify the right side.

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Step 2.3.3.3.1

Divide $- 11$ by $- 1$ .

$x = 11$