Calculus Examples

$\log_{2} (\frac{s^{5}}{9 t^{2}})$

Step 1

Rewrite $\log_{2} (\frac{s^{5}}{9 t^{2}})$ as $\log_{2} (s^{5}) - \log_{2} (9 t^{2})$ .

$\log_{2} (s^{5}) - \log_{2} (9 t^{2})$

Step 2

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

$5 \log_{2} (s) - \log_{2} (9 t^{2})$

Step 3

Rewrite $\log_{2} (9 t^{2})$ as $\log_{2} (9) + \log_{2} (t^{2})$ .

$5 \log_{2} (s) - (\log_{2} (9) + \log_{2} (t^{2}))$

Step 4

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

$5 \log_{2} (s) - (\log_{2} (9) + 2 \log_{2} (t))$

Step 5

Simplify each term.

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Simplify each term.

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Rewrite $\log_{2} (9)$ as $\log_{2} (3^{2})$ .

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

Expand $\log_{2} (3^{2})$ by moving $2$ outside the logarithm.

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

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Multiply $2$ by $- 1$ .

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