Precalculus Examples

$\log_{2} (\frac{6 x}{y})$

Step 1

Rewrite $\log_{2} (\frac{6 x}{y})$ as $\log_{2} (6 x) - \log_{2} (y)$ .

$\log_{2} (6 x) - \log_{2} (y)$

Step 2

Rewrite $\log_{2} (6 x)$ as $\log_{2} (6) + \log_{2} (x)$ .

$\log_{2} (6) + \log_{2} (x) - \log_{2} (y)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{2} (6)$ as $\log_{2} (2 (3))$ .

$\log_{2} (2 (3)) + \log_{2} (x) - \log_{2} (y)$

Step 3.2

Rewrite $\log_{2} (2 (3))$ as $\log_{2} (2) + \log_{2} (3)$ .

$\log_{2} (2) + \log_{2} (3) + \log_{2} (x) - \log_{2} (y)$

Step 3.3

Logarithm base $2$ of $2$ is $1$ .

$1 + \log_{2} (3) + \log_{2} (x) - \log_{2} (y)$