Algebra Examples

$\log (\frac{5 x^{3}}{2 x y^{3}})$

Step 1

Rewrite $\log (\frac{5 x^{3}}{2 x y^{3}})$ as $\log (5 x^{3}) - \log (2 x y^{3})$ .

$\log (5 x^{3}) - \log (2 x y^{3})$

Step 2

Rewrite $\log (5 x^{3})$ as $\log (5) + \log (x^{3})$ .

$\log (5) + \log (x^{3}) - \log (2 x y^{3})$

Step 3

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

$\log (5) + 3 \log (x) - \log (2 x y^{3})$

Step 4

Rewrite $\log (2 x y^{3})$ as $\log (2 x) + \log (y^{3})$ .

$\log (5) + 3 \log (x) - (\log (2 x) + \log (y^{3}))$

Step 5

Rewrite $\log (2 x)$ as $\log (2) + \log (x)$ .

$\log (5) + 3 \log (x) - (\log (2) + \log (x) + \log (y^{3}))$

Step 6

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

$\log (5) + 3 \log (x) - (\log (2) + \log (x) + 3 \log (y))$

Step 7

Simplify each term.

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Step 7.1

Apply the distributive property.

$\log (5) + 3 \log (x) - \log (2) - \log (x) - (3 \log (y))$

Step 7.2

Multiply $3$ by $- 1$ .

$\log (5) + 3 \log (x) - \log (2) - \log (x) - 3 \log (y)$

Step 8

Subtract $\log (x)$ from $3 \log (x)$ .

$\log (5) + 2 \log (x) - \log (2) - 3 \log (y)$