Write as a Single Logarithm 4* log of x-(2* log of v+3* log of y)

$4 \cdot \log (x) - (2 \cdot \log (v) + 3 \cdot \log (y))$

Step 1

Simplify each term.

Simplify $4 \log (x)$ by moving $4$ inside the logarithm.

$\log (x^{4}) - (2 \cdot \log (v) + 3 \cdot \log (y))$

Simplify each term.

Simplify $2 \log (v)$ by moving $2$ inside the logarithm.

$\log (x^{4}) - (\log (v^{2}) + 3 \cdot \log (y))$

Simplify $3 \log (y)$ by moving $3$ inside the logarithm.

$\log (x^{4}) - (\log (v^{2}) + \log (y^{3}))$

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x^{4}) - \log (v^{2} y^{3})$

Step 2

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

$\log (\frac{x^{4}}{v^{2} y^{3}})$