Write as a Single Logarithm log of x+5 log of y- log of m

$\log (x) + 5 \log (y) - \log (m)$

Step 1

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

$5 \log (y) + \log (\frac{x}{m})$

Step 2

Simplify $5 \log (y)$ by moving $5$ inside the logarithm.

$\log (y^{5}) + \log (\frac{x}{m})$

Step 3

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

$\log (y^{5} \frac{x}{m})$

Step 4

Combine $y^{5}$ and $\frac{x}{m}$ .

$\log (\frac{y^{5} x}{m})$