Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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

Step 3

Multiply $2$ by $25$ .

$\log_{b} (50)$