Solve for x log of x+11 = log of x+ log of 11

$\log (x + 11) = \log (x) + \log (11)$

Step 1

Simplify the right side.

Simplify $\log (x) + \log (11)$ .

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x + 11) = \log (x \cdot 11)$

Move $11$ to the left of $x$ .

$\log (x + 11) = \log (11 x)$

Step 2

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

$x + 11 = 11 x$

Step 3

Solve for $x$ .

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

Subtract $11 x$ from both sides of the equation.

$x + 11 - 11 x = 0$

Subtract $11 x$ from $x$ .

$- 10 x + 11 = 0$

Subtract $11$ from both sides of the equation.

$- 10 x = - 11$

Divide each term in $- 10 x = - 11$ by $- 10$ and simplify.

Divide each term in $- 10 x = - 11$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 11}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 11}{- 10}$

Divide $x$ by $1$ .

$x = \frac{- 11}{- 10}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{11}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{10}$

Decimal Form:

$x = 1.1$

Mixed Number Form:

$x = 1 \frac{1}{10}$