Solve for x log of x+7 = log of x+ log of 7

$\log (x + 7) = \log (x) + \log (7)$

Simplify the right side.

Simplify $\log (x) + \log (7)$ .

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

$\log (x + 7) = \log (x \cdot 7)$

Move $7$ to the left of $x$ .

$\log (x + 7) = \log (7 x)$

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

$x + 7 = 7 x$

Solve for $x$ .

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

Subtract $7 x$ from both sides of the equation.

$x + 7 - 7 x = 0$

Subtract $7 x$ from $x$ .

$- 6 x + 7 = 0$

Subtract $7$ from both sides of the equation.

$- 6 x = - 7$

Divide each term in $- 6 x = - 7$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 7$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 7}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 7}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 6}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{7}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{6}$

Decimal Form:

$x = 1.1\overline{6}$

Mixed Number Form:

$x = 1 \frac{1}{6}$