Solve for x log of x+ log of 7 = log of 37

$\log (x) + \log (7) = \log (37)$

Simplify the left side.

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

$\log (x \cdot 7) = \log (37)$

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

$\log (7 x) = \log (37)$

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

$7 x = 37$

Divide each term in $7 x = 37$ by $7$ and simplify.

Divide each term in $7 x = 37$ by $7$ .

$\frac{7 x}{7} = \frac{37}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{37}{7}$

Divide $x$ by $1$ .

$x = \frac{37}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{37}{7}$

Decimal Form:

$x = 5.\overline{285714}$

Mixed Number Form:

$x = 5 \frac{2}{7}$