Solve for x log of x+10 = log of x+ log of 10

$\log (x + 10) = \log (x) + \log (10)$

Step 1

Simplify the right side.

Simplify $\log (x) + \log (10)$ .

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

$\log (x + 10) = \log (x \cdot 10)$

Move $10$ to the left of $x$ .

$\log (x + 10) = \log (10 x)$

Step 2

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

$x + 10 = 10 x$

Step 3

Solve for $x$ .

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

Subtract $10 x$ from both sides of the equation.

$x + 10 - 10 x = 0$

Subtract $10 x$ from $x$ .

$- 9 x + 10 = 0$

Subtract $10$ from both sides of the equation.

$- 9 x = - 10$

Divide each term in $- 9 x = - 10$ by $- 9$ and simplify.

Divide each term in $- 9 x = - 10$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 10}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 10}{- 9}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 9}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{10}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{9}$

Decimal Form:

$x = 1.\overline{1}$

Mixed Number Form:

$x = 1 \frac{1}{9}$