Precalculus Examples

$\log_{6} (144) - \log_{6} (12) + \log_{6} (3)$

Step 1

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

$\log_{6} (\frac{144}{12}) + \log_{6} (3)$

Step 2

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

$\log_{6} (\frac{144}{12} \cdot 3)$

Step 3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1

Factor $3$ out of $12$ .

$\log_{6} (\frac{144}{3 (4)} \cdot 3)$

Step 3.2

Cancel the common factor.

$\log_{6} (\frac{144}{3 \cdot 4} \cdot 3)$

Step 3.3

Rewrite the expression.

$\log_{6} (\frac{144}{4})$

Step 4

Logarithm base $6$ of $\frac{144}{4}$ is $2$ .

$2$