Expand the Logarithmic Expression log of (s square root of 7)/(t^2)

$\log (\frac{s \sqrt{7}}{t^{2}})$

Step 1

Rewrite $\log (\frac{s \sqrt{7}}{t^{2}})$ as $\log (s \sqrt{7}) - \log (t^{2})$ .

$\log (s \sqrt{7}) - \log (t^{2})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\log (s \cdot 7^{\frac{1}{2}}) - \log (t^{2})$

Step 3

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

$\log (s \cdot 7^{\frac{1}{2}}) - (2 \log (t))$

Step 4

Multiply $2$ by $- 1$ .

$\log (s \cdot 7^{\frac{1}{2}}) - 2 \log (t)$

Step 5

Rewrite $\log (s \cdot 7^{\frac{1}{2}})$ as $\log (s) + \log (7^{\frac{1}{2}})$ .

$\log (s) + \log (7^{\frac{1}{2}}) - 2 \log (t)$

Step 6

Expand $\log (7^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\log (s) + \frac{1}{2} \log (7) - 2 \log (t)$

Step 7

Combine $\frac{1}{2}$ and $\log (7)$ .

$\log (s) + \frac{\log (7)}{2} - 2 \log (t)$