Expand the Logarithmic Expression log of (100 square root of y)/(z^3)

$\log (\frac{100 \sqrt{y}}{z^{3}})$

Step 1

Rewrite $\log (\frac{100 \sqrt{y}}{z^{3}})$ as $\log (100 \sqrt{y}) - \log (z^{3})$ .

$\log (100 \sqrt{y}) - \log (z^{3})$

Step 2

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

$\log (100 y^{\frac{1}{2}}) - \log (z^{3})$

Step 3

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

$\log (100 y^{\frac{1}{2}}) - (3 \log (z))$

Step 4

Multiply $3$ by $- 1$ .

$\log (100 y^{\frac{1}{2}}) - 3 \log (z)$

Step 5

Rewrite $\log (100 y^{\frac{1}{2}})$ as $\log (100) + \log (y^{\frac{1}{2}})$ .

$\log (100) + \log (y^{\frac{1}{2}}) - 3 \log (z)$

Step 6

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

$\log (100) + \frac{1}{2} \log (y) - 3 \log (z)$

Step 7

Logarithm base $10$ of $100$ is $2$ .

$2 + \frac{1}{2} \log (y) - 3 \log (z)$

Step 8

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

$2 + \frac{\log (y)}{2} - 3 \log (z)$