Write as a Single Logarithm log base 2 of x- log base 2 of y-3 log base 2 of z

$\log_{2} (x) - \log_{2} (y) - 3 \log_{2} (z)$

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

$\log_{2} (\frac{x}{y}) - 3 \log_{2} (z)$

Simplify $- 3 \log_{2} (z)$ by moving $3$ inside the logarithm.

$\log_{2} (\frac{x}{y}) - \log_{2} (z^{3})$

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

$\log_{2} (\frac{\frac{x}{y}}{z^{3}})$

Multiply the numerator by the reciprocal of the denominator.

$\log_{2} (\frac{x}{y} \cdot \frac{1}{z^{3}})$

Combine.

$\log_{2} (\frac{x \cdot 1}{y z^{3}})$

Multiply $x$ by $1$ .

$\log_{2} (\frac{x}{y z^{3}})$