Solve for x log of 7-x- log of 3x+2=1

$\log (7 - x) - \log (3 x + 2) = 1$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{7 - x}{3 x + 2}) = 1$

Rewrite $\log (\frac{7 - x}{3 x + 2}) = 1$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ $\neq$ $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{1} = \frac{7 - x}{3 x + 2}$

Cross multiply to remove the fraction.

$7 - x = 10 (3 x + 2)$

Simplify $10 (3 x + 2)$ .

Apply the distributive property.

$7 - x = 10 (3 x) + 10 \cdot 2$

Multiply.

Multiply $3$ by $10$ .

$7 - x = 30 x + 10 \cdot 2$

Multiply $10$ by $2$ .

$7 - x = 30 x + 20$

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

Subtract $30 x$ from both sides of the equation.

$7 - x - 30 x = 20$

Subtract $30 x$ from $- x$ .

$7 - 31 x = 20$

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- 31 x = 20 - 7$

Subtract $7$ from $20$ .

$- 31 x = 13$

Divide each term in $- 31 x = 13$ by $- 31$ and simplify.

Divide each term in $- 31 x = 13$ by $- 31$ .

$\frac{- 31 x}{- 31} = \frac{13}{- 31}$

Simplify the left side.

Cancel the common factor of $- 31$ .

Cancel the common factor.

$\frac{- 31 x}{- 31} = \frac{13}{- 31}$

Divide $x$ by $1$ .

$x = \frac{13}{- 31}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{13}{31}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{31}$

Decimal Form:

$x = - 0.41935483 \dots$

Solve for x log of 7-x- log of 3x+2=1

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