Algebra Examples

$\log_{5} (6) - \log_{5} (2) = \log_{5} (3)$

Step 1

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

$\log_{5} (\frac{6}{2}) = \log_{5} (3)$

Step 2

Divide $6$ by $2$ .

$\log_{5} (3) = \log_{5} (3)$

Step 3

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

$\log_{5} (6) - \log_{5} (2) = \log_{5} (3)$ is an identity.