Precalculus Examples

$\log (\frac{6}{5}) \cdot 6$

Step 1

Rewrite $\log (\frac{6}{5})$ as $\log (6) - \log (5)$ .

$(\log (6) - \log (5)) \cdot 6$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Rewrite $\log (6)$ as $\log (2 (3))$ .

$(\log (2 (3)) - \log (5)) \cdot 6$

Step 2.2

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$(\log (2) + \log (3) - \log (5)) \cdot 6$

Step 3

Apply the distributive property.

$\log (2) \cdot 6 + \log (3) \cdot 6 - \log (5) \cdot 6$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Move $6$ to the left of $\log (2)$ .

$6 \cdot \log (2) + \log (3) \cdot 6 - \log (5) \cdot 6$

Step 4.2

Move $6$ to the left of $\log (3)$ .

$6 \cdot \log (2) + 6 \cdot \log (3) - \log (5) \cdot 6$

Step 4.3

Multiply $6$ by $- 1$ .

$6 \cdot \log (2) + 6 \cdot \log (3) - 6 \log (5)$

Step 5

Multiply $6$ by $\log (3)$ .

$6 \log (2) + 6 \log (3) - 6 \log (5)$