Solve for m log base 2 of m = log base 2 of m+5- log base 2 of 3

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

Step 1

Simplify the right side.

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

$\log_{2} (m) = \log_{2} (\frac{m + 5}{3})$

Step 2

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

$m = \frac{m + 5}{3}$

Step 3

Solve for $m$ .

Multiply both sides by $3$ .

$m \cdot 3 = \frac{m + 5}{3} \cdot 3$

Simplify.

Simplify the left side.

Move $3$ to the left of $m$ .

$3 m = \frac{m + 5}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 m = \frac{m + 5}{3} \cdot 3$

Rewrite the expression.

$3 m = m + 5$

Solve for $m$ .

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

Subtract $m$ from both sides of the equation.

$3 m - m = 5$

Subtract $m$ from $3 m$ .

$2 m = 5$

Divide each term in $2 m = 5$ by $2$ and simplify.

Divide each term in $2 m = 5$ by $2$ .

$\frac{2 m}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 m}{2} = \frac{5}{2}$

Divide $m$ by $1$ .

$m = \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = \frac{5}{2}$

Decimal Form:

$m = 2.5$

Mixed Number Form:

$m = 2 \frac{1}{2}$