Algebra Examples

$\log (\frac{2 {(x + 7)}^{5}}{\sqrt[3]{x^{4}}})$

Rewrite $\log (\frac{2 {(x + 7)}^{5}}{\sqrt[3]{x^{4}}})$ as $\log (2 {(x + 7)}^{5}) - \log (\sqrt[3]{x^{4}})$ .

$\log (2 {(x + 7)}^{5}) - \log (\sqrt[3]{x^{4}})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{4}}$ as $x^{\frac{4}{3}}$ .

$\log (2 {(x + 7)}^{5}) - \log (x^{\frac{4}{3}})$

Expand $\log (x^{\frac{4}{3}})$ by moving $\frac{4}{3}$ outside the logarithm.

$\log (2 {(x + 7)}^{5}) - (\frac{4}{3} \log (x))$

Combine $\frac{4}{3}$ and $\log (x)$ .

$\log (2 {(x + 7)}^{5}) - \frac{4 \log (x)}{3}$

Rewrite $\log (2 {(x + 7)}^{5})$ as $\log (2) + \log ({(x + 7)}^{5})$ .

$\log (2) + \log ({(x + 7)}^{5}) - \frac{4 \log (x)}{3}$

Expand $\log ({(x + 7)}^{5})$ by moving $5$ outside the logarithm.

$\log (2) + 5 \log (x + 7) - \frac{4 \log (x)}{3}$

To write $5 \log (x + 7)$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\log (2) + 5 \log (x + 7) \cdot \frac{3}{3} - \frac{4 \log (x)}{3}$

Combine $5 \log (x + 7)$ and $\frac{3}{3}$ .

$\log (2) + \frac{5 \log (x + 7) \cdot 3}{3} - \frac{4 \log (x)}{3}$

Combine the numerators over the common denominator.

$\log (2) + \frac{5 \log (x + 7) \cdot 3 - 4 \log (x)}{3}$

Multiply $3$ by $5$ .

$\log (2) + \frac{15 \log (x + 7) - 4 \log (x)}{3}$