Expand the Logarithmic Expression log base 4 of ((2j)/(k^5))^3

$\log_{4} ({(\frac{2 j}{k^{5}})}^{3})$

Step 1

Expand $\log_{4} ({(\frac{2 j}{k^{5}})}^{3})$ by moving $3$ outside the logarithm.

$3 \log_{4} (\frac{2 j}{k^{5}})$

Step 2

Rewrite $\log_{4} (\frac{2 j}{k^{5}})$ as $\log_{4} (2 j) - \log_{4} (k^{5})$ .

$3 (\log_{4} (2 j) - \log_{4} (k^{5}))$

Step 3

Expand $\log_{4} (k^{5})$ by moving $5$ outside the logarithm.

$3 (\log_{4} (2 j) - (5 \log_{4} (k)))$

Step 4

Multiply $5$ by $- 1$ .

$3 (\log_{4} (2 j) - 5 \log_{4} (k))$

Step 5

Rewrite $\log_{4} (2 j)$ as $\log_{4} (2) + \log_{4} (j)$ .

$3 (\log_{4} (2) + \log_{4} (j) - 5 \log_{4} (k))$

Step 6

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$3 (\frac{1}{2} + \log_{4} (j) - 5 \log_{4} (k))$

Step 7

Apply the distributive property.

$3 (\frac{1}{2}) + 3 \log_{4} (j) + 3 (- 5 \log_{4} (k))$

Step 8

Simplify.

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} + 3 \log_{4} (j) + 3 (- 5 \log_{4} (k))$

Multiply $- 5$ by $3$ .

$\frac{3}{2} + 3 \log_{4} (j) - 15 \log_{4} (k)$