Algebra Examples

$\log_{6} (18) - \log_{6} (6) = \log_{6} (3)$

Step 1

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

$\log_{6} (\frac{18}{6}) = \log_{6} (3)$

Step 2

Divide $18$ by $6$ .

$\log_{6} (3) = \log_{6} (3)$

Step 3

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

$\log_{6} (18) - \log_{6} (6) = \log_{6} (3)$ is an identity.