Trigonometry Examples

$\log_{g} (\frac{\sqrt{s} t^{5}}{r^{8}})$

Step 1

Rewrite $\log_{g} (\frac{\sqrt{s} t^{5}}{r^{8}})$ as $\log_{g} (\sqrt{s} t^{5}) - \log_{g} (r^{8})$ .

$\log_{g} (\sqrt{s} t^{5}) - \log_{g} (r^{8})$

Step 2

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

$\log_{g} (s^{\frac{1}{2}} t^{5}) - \log_{g} (r^{8})$

Step 3

Expand $\log_{g} (r^{8})$ by moving $8$ outside the logarithm.

$\log_{g} (s^{\frac{1}{2}} t^{5}) - (8 \log_{g} (r))$

Step 4

Multiply $8$ by $- 1$ .

$\log_{g} (s^{\frac{1}{2}} t^{5}) - 8 \log_{g} (r)$

Step 5

Rewrite $\log_{g} (s^{\frac{1}{2}} t^{5})$ as $\log_{g} (s^{\frac{1}{2}}) + \log_{g} (t^{5})$ .

$\log_{g} (s^{\frac{1}{2}}) + \log_{g} (t^{5}) - 8 \log_{g} (r)$

Step 6

Expand $\log_{g} (s^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{g} (s) + \log_{g} (t^{5}) - 8 \log_{g} (r)$

Step 7

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

$\frac{1}{2} \log_{g} (s) + 5 \log_{g} (t) - 8 \log_{g} (r)$

Step 8

Combine $\frac{1}{2}$ and $\log_{g} (s)$ .

$\frac{\log_{g} (s)}{2} + 5 \log_{g} (t) - 8 \log_{g} (r)$