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

$\log_{b} (2) + 2 \log_{b} (5)$

Simplify each term.

Simplify $2 \log_{b} (5)$ by moving $2$ inside the logarithm.

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

Raise $5$ to the power of $2$ .

$\log_{b} (2) + \log_{b} (25)$

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

$\log_{b} (2 \cdot 25)$

Multiply $2$ by $25$ .

$\log_{b} (50)$