Solve for x log base 2 of -45x-185- log base 2 of 5=3

$\log_{2} (- 45 x - 185) - \log_{2} (5) = 3$

Simplify the left side.

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

$\log_{2} (\frac{- 45 x - 185}{5}) = 3$

Cancel the common factor of $- 45 x - 185$ and $5$ .

Factor $5$ out of $- 45 x$ .

$\log_{2} (\frac{5 (- 9 x) - 185}{5}) = 3$

Factor $5$ out of $- 185$ .

$\log_{2} (\frac{5 (- 9 x) + 5 \cdot - 37}{5}) = 3$

Factor $5$ out of $5 (- 9 x) + 5 (- 37)$ .

$\log_{2} (\frac{5 (- 9 x - 37)}{5}) = 3$

Cancel the common factors.

Factor $5$ out of $5$ .

$\log_{2} (\frac{5 (- 9 x - 37)}{5 (1)}) = 3$

Cancel the common factor.

$\log_{2} (\frac{5 (- 9 x - 37)}{5 \cdot 1}) = 3$

Rewrite the expression.

$\log_{2} (\frac{- 9 x - 37}{1}) = 3$

Divide $- 9 x - 37$ by $1$ .

$\log_{2} (- 9 x - 37) = 3$

Rewrite $\log_{2} (- 9 x - 37) = 3$ 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 $b^{y} = x$ .

$2^{3} = - 9 x - 37$

Solve for $x$ .

Rewrite the equation as $- 9 x - 37 = 2^{3}$ .

$- 9 x - 37 = 2^{3}$

Raise $2$ to the power of $3$ .

$- 9 x - 37 = 8$

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

Add $37$ to both sides of the equation.

$- 9 x = 8 + 37$

Add $8$ and $37$ .

$- 9 x = 45$

Divide each term in $- 9 x = 45$ by $- 9$ and simplify.

Divide each term in $- 9 x = 45$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{45}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{45}{- 9}$

Divide $x$ by $1$ .

$x = \frac{45}{- 9}$

Simplify the right side.

Divide $45$ by $- 9$ .

$x = - 5$

Solve for x log base 2 of -45x-185- log base 2 of 5=3

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