Solve for x log of x+5 = log of x+ log of 5

$\log (x + 5) = \log (x) + \log (5)$

Step 1

Simplify the right side.

Simplify $\log (x) + \log (5)$ .

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

$\log (x + 5) = \log (x \cdot 5)$

Move $5$ to the left of $x$ .

$\log (x + 5) = \log (5 x)$

Step 2

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

$x + 5 = 5 x$

Step 3

Solve for $x$ .

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

Subtract $5 x$ from both sides of the equation.

$x + 5 - 5 x = 0$

Subtract $5 x$ from $x$ .

$- 4 x + 5 = 0$

Subtract $5$ from both sides of the equation.

$- 4 x = - 5$

Divide each term in $- 4 x = - 5$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 5$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 5}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 5}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{4}$

Decimal Form:

$x = 1.25$

Mixed Number Form:

$x = 1 \frac{1}{4}$