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

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

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

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

Rewrite $\log (\frac{2 x}{x - 3}) = 1$ 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 $b^{y} = x$ .

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

Cross multiply to remove the fraction.

$2 x = 10 (x - 3)$

Simplify $10 (x - 3)$ .

Apply the distributive property.

$2 x = 10 x + 10 \cdot - 3$

Multiply $10$ by $- 3$ .

$2 x = 10 x - 30$

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

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

$2 x - 10 x = - 30$

Subtract $10 x$ from $2 x$ .

$- 8 x = - 30$

Divide each term in $- 8 x = - 30$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 30$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 30}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 30}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 30}{- 8}$

Simplify the right side.

Cancel the common factor of $- 30$ and $- 8$ .

Factor $- 2$ out of $- 30$ .

$x = \frac{- 2 (15)}{- 8}$

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

$x = \frac{- 2 \cdot 15}{- 2 \cdot 4}$

Cancel the common factor.

$x = \frac{- 2 \cdot 15}{- 2 \cdot 4}$

Rewrite the expression.

$x = \frac{15}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{4}$

Decimal Form:

$x = 3.75$

Mixed Number Form:

$x = 3 \frac{3}{4}$

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

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