Solve for y log of 6- log of -2y-3 = log of 4

$\log (6) - \log (- 2 y - 3) = \log (4)$

Step 1

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

$\log (\frac{6}{- 2 y - 3}) = \log (4)$

Step 2

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

$\frac{6}{- 2 y - 3} = 4$

Step 3

Solve for $y$ .

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$- 2 y - 3, 1$

Remove parentheses.

$- 2 y - 3, 1$

The LCM of one and any expression is the expression.

$- 2 y - 3$

Multiply each term in $\frac{6}{- 2 y - 3} = 4$ by $- 2 y - 3$ to eliminate the fractions.

Multiply each term in $\frac{6}{- 2 y - 3} = 4$ by $- 2 y - 3$ .

$\frac{6}{- 2 y - 3} (- 2 y - 3) = 4 (- 2 y - 3)$

Simplify the left side.

Multiply $\frac{6}{- 2 y - 3}$ by $- 2 y - 3$ .

$\frac{6 (- 2 y - 3)}{- 2 y - 3} = 4 (- 2 y - 3)$

Cancel the common factor of $- 2 y - 3$ .

Cancel the common factor.

$\frac{6 (- 2 y - 3)}{- 2 y - 3} = 4 (- 2 y - 3)$

Divide $6$ by $1$ .

$6 = 4 (- 2 y - 3)$

Simplify the right side.

Apply the distributive property.

$6 = 4 (- 2 y) + 4 \cdot - 3$

Multiply.

Multiply $- 2$ by $4$ .

$6 = - 8 y + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$6 = - 8 y - 12$

Solve the equation.

Rewrite the equation as $- 8 y - 12 = 6$ .

$- 8 y - 12 = 6$

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

Add $12$ to both sides of the equation.

$- 8 y = 6 + 12$

Add $6$ and $12$ .

$- 8 y = 18$

Divide each term in $- 8 y = 18$ by $- 8$ and simplify.

Divide each term in $- 8 y = 18$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{18}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{18}{- 8}$

Divide $y$ by $1$ .

$y = \frac{18}{- 8}$

Simplify the right side.

Cancel the common factor of $18$ and $- 8$ .

Factor $2$ out of $18$ .

$y = \frac{2 (9)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$y = \frac{2 \cdot 9}{2 \cdot - 4}$

Cancel the common factor.

$y = \frac{2 \cdot 9}{2 \cdot - 4}$

Rewrite the expression.

$y = \frac{9}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{9}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{9}{4}$

Decimal Form:

$y = - 2.25$

Mixed Number Form:

$y = - 2 \frac{1}{4}$

Solve for y log of 6- log of -2y-3 = log of 4

Related Questions

Support LCMGCF.com by disabling your adblocker.