Write as a Single Logarithm 5* log of a+1/2* log of b-4* log of c

$5 \cdot \log (a) + \frac{1}{2} \cdot \log (b) - 4 \cdot \log (c)$

Simplify each term.

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

$\log (a^{5}) + \frac{1}{2} \cdot \log (b) - 4 \cdot \log (c)$

Simplify $\frac{1}{2} \log (b)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (a^{5}) + \log (b^{\frac{1}{2}}) - 4 \cdot \log (c)$

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

$\log (a^{5}) + \log (b^{\frac{1}{2}}) - \log (c^{4})$

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

$\log (a^{5} b^{\frac{1}{2}}) - \log (c^{4})$

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

$\log (\frac{a^{5} b^{\frac{1}{2}}}{c^{4}})$