Write as a Single Logarithm 5 log base b of x+1/2 log base b of x+2

$5 \log_{b} (x) + \frac{1}{2} \log_{b} (x + 2)$

Step 1

Simplify each term.

Simplify $5 \log_{b} (x)$ by moving $5$ inside the logarithm.

$\log_{b} (x^{5}) + \frac{1}{2} \cdot \log_{b} (x + 2)$

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

$\log_{b} (x^{5}) + \log_{b} ({(x + 2)}^{\frac{1}{2}})$

Step 2

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

$\log_{b} (x^{5} {(x + 2)}^{\frac{1}{2}})$