Algebra Examples

$\log (\frac{2 x^{2} y}{3 k^{3}})$

Step 1

Rewrite $\log (\frac{2 x^{2} y}{3 k^{3}})$ as $\log (2 x^{2} y) - \log (3 k^{3})$ .

$\log (2 x^{2} y) - \log (3 k^{3})$

Step 2

Rewrite $\log (2 x^{2} y)$ as $\log (2 x^{2}) + \log (y)$ .

$\log (2 x^{2}) + \log (y) - \log (3 k^{3})$

Step 3

Rewrite $\log (2 x^{2})$ as $\log (2) + \log (x^{2})$ .

$\log (2) + \log (x^{2}) + \log (y) - \log (3 k^{3})$

Step 4

Expand $\log (x^{2})$ by moving $2$ outside the logarithm.

$\log (2) + 2 \log (x) + \log (y) - \log (3 k^{3})$

Step 5

Rewrite $\log (3 k^{3})$ as $\log (3) + \log (k^{3})$ .

$\log (2) + 2 \log (x) + \log (y) - (\log (3) + \log (k^{3}))$

Step 6

Expand $\log (k^{3})$ by moving $3$ outside the logarithm.

$\log (2) + 2 \log (x) + \log (y) - (\log (3) + 3 \log (k))$

Step 7

Simplify each term.

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Step 7.1

Apply the distributive property.

$\log (2) + 2 \log (x) + \log (y) - \log (3) - (3 \log (k))$

Step 7.2

Multiply $3$ by $- 1$ .

$\log (2) + 2 \log (x) + \log (y) - \log (3) - 3 \log (k)$