Solve for n log base 2 of 5n+8 = log base 2 of -3n

$\log_{2} (5 n + 8) = \log_{2} (- 3 n)$

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

$5 n + 8 = - 3 n$

Solve for $n$ .

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

Add $3 n$ to both sides of the equation.

$5 n + 8 + 3 n = 0$

Add $5 n$ and $3 n$ .

$8 n + 8 = 0$

Subtract $8$ from both sides of the equation.

$8 n = - 8$

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

Divide each term in $8 n = - 8$ by $8$ .

$\frac{8 n}{8} = \frac{- 8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 n}{8} = \frac{- 8}{8}$

Divide $n$ by $1$ .

$n = \frac{- 8}{8}$

Simplify the right side.

Divide $- 8$ by $8$ .

$n = - 1$