Simplify/Condense log of 3+1/2* log of x- log of 5

$\log (3) + \frac{1}{2} \cdot \log (x) - \log (5)$

Step 1

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

$\frac{1}{2} \cdot \log (x) + \log (\frac{3}{5})$

Step 2

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

$\log (x^{\frac{1}{2}}) + \log (\frac{3}{5})$

Step 3

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

$\log (x^{\frac{1}{2}} \frac{3}{5})$

Step 4

Combine $x^{\frac{1}{2}}$ and $\frac{3}{5}$ .

$\log (\frac{x^{\frac{1}{2}} \cdot 3}{5})$

Step 5

Move $3$ to the left of $x^{\frac{1}{2}}$ .

$\log (\frac{3 x^{\frac{1}{2}}}{5})$