Algebra Examples

$\log_{\frac{1}{2}} (\frac{3 x^{2}}{2})$

Step 1

Rewrite $\log_{\frac{1}{2}} (\frac{3 x^{2}}{2})$ as $\log_{\frac{1}{2}} (3 x^{2}) - \log_{\frac{1}{2}} (2)$ .

$\log_{\frac{1}{2}} (3 x^{2}) - \log_{\frac{1}{2}} (2)$

Step 2

Logarithm base $\frac{1}{2}$ of $2$ is $- 1$ .

$\log_{\frac{1}{2}} (3 x^{2}) - - 1$

Step 3

Multiply $- 1$ by $- 1$ .

$\log_{\frac{1}{2}} (3 x^{2}) + 1$

Step 4

Rewrite $\log_{\frac{1}{2}} (3 x^{2})$ as $\log_{\frac{1}{2}} (3) + \log_{\frac{1}{2}} (x^{2})$ .

$\log_{\frac{1}{2}} (3) + \log_{\frac{1}{2}} (x^{2}) + 1$

Step 5

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

$\log_{\frac{1}{2}} (3) + 2 \log_{\frac{1}{2}} (x) + 1$