Calculus Examples

$\log_{2} (\frac{s^{5}}{6 t^{2}})$

Step 1

Rewrite $\log_{2} (\frac{s^{5}}{6 t^{2}})$ as $\log_{2} (s^{5}) - \log_{2} (6 t^{2})$ .

$\log_{2} (s^{5}) - \log_{2} (6 t^{2})$

Step 2

Expand $\log_{2} (s^{5})$ by moving $5$ outside the logarithm.

$5 \log_{2} (s) - \log_{2} (6 t^{2})$

Step 3

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

$5 \log_{2} (s) - (\log_{2} (6) + \log_{2} (t^{2}))$

Step 4

Expand $\log_{2} (t^{2})$ by moving $2$ outside the logarithm.

$5 \log_{2} (s) - (\log_{2} (6) + 2 \log_{2} (t))$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

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

$5 \log_{2} (s) - (\log_{2} (2 (3)) + 2 \log_{2} (t))$

Step 5.1.2

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

$5 \log_{2} (s) - (\log_{2} (2) + \log_{2} (3) + 2 \log_{2} (t))$

Step 5.1.3

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

$5 \log_{2} (s) - (1 + \log_{2} (3) + 2 \log_{2} (t))$

Step 5.2

Apply the distributive property.

$5 \log_{2} (s) - 1 \cdot 1 - \log_{2} (3) - (2 \log_{2} (t))$

Step 5.3

Simplify.

Tap for more steps...

Step 5.3.1

Multiply $- 1$ by $1$ .

$5 \log_{2} (s) - 1 - \log_{2} (3) - (2 \log_{2} (t))$

Step 5.3.2

Multiply $2$ by $- 1$ .

$5 \log_{2} (s) - 1 - \log_{2} (3) - 2 \log_{2} (t)$