Algebra Examples

$\log_{2} (10) + \log_{2} (4) = \log_{2} (40)$

Step 1

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

$\log_{2} (10 \cdot 4) = \log_{2} (40)$

Step 2

Multiply $10$ by $4$ .

$\log_{2} (40) = \log_{2} (40)$

Step 3

Since the two sides have been shown to be equivalent, the equation is an identity.

$\log_{2} (10) + \log_{2} (4) = \log_{2} (40)$ is an identity.