Precalculus Examples

$\log_{2} ({(\frac{6}{7^{5}})}^{6})$

Step 1

Expand $\log_{2} ({(\frac{6}{7^{5}})}^{6})$ by moving $6$ outside the logarithm.

$6 \log_{2} (\frac{6}{7^{5}})$

Step 2

Raise $7$ to the power of $5$ .

$6 \log_{2} (\frac{6}{16807})$

Step 3

Rewrite $\log_{2} (\frac{6}{16807})$ as $\log_{2} (6) - \log_{2} (16807)$ .

$6 (\log_{2} (6) - \log_{2} (16807))$

Step 4

Rewrite $\log_{2} (16807)$ as $\log_{2} (7^{5})$ .

$6 (\log_{2} (6) - \log_{2} (7^{5}))$

Step 5

Expand $\log_{2} (7^{5})$ by moving $5$ outside the logarithm.

$6 (\log_{2} (6) - (5 \log_{2} (7)))$

Step 6

Multiply $5$ by $- 1$ .

$6 (\log_{2} (6) - 5 \log_{2} (7))$

Step 7

Simplify each term.

Tap for more steps...

Step 7.1

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

$6 (\log_{2} (2 (3)) - 5 \log_{2} (7))$

Step 7.2

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

$6 (\log_{2} (2) + \log_{2} (3) - 5 \log_{2} (7))$

Step 7.3

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

$6 (1 + \log_{2} (3) - 5 \log_{2} (7))$

Step 8

Apply the distributive property.

$6 \cdot 1 + 6 \log_{2} (3) + 6 (- 5 \log_{2} (7))$

Step 9

Simplify.

Tap for more steps...

Step 9.1

Multiply $6$ by $1$ .

$6 + 6 \log_{2} (3) + 6 (- 5 \log_{2} (7))$

Step 9.2

Multiply $- 5$ by $6$ .

$6 + 6 \log_{2} (3) - 30 \log_{2} (7)$