Precalculus Examples

$2 \log (3) - \frac{1}{2} \cdot \log (x^{2} + 1)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $2 \log (3)$ by moving $2$ inside the logarithm.

$\log (3^{2}) - \frac{1}{2} \cdot \log (x^{2} + 1)$

Step 1.2

Raise $3$ to the power of $2$ .

$\log (9) - \frac{1}{2} \cdot \log (x^{2} + 1)$

Step 1.3

Multiply $- \frac{1}{2} \log (x^{2} + 1)$ .

Tap for more steps...

Step 1.3.1

Reorder $\log (x^{2} + 1)$ and $\frac{1}{2}$ .

$\log (9) - (\frac{1}{2} \log (x^{2} + 1))$

Step 1.3.2

Simplify $\frac{1}{2} \log (x^{2} + 1)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (9) - \log ({(x^{2} + 1)}^{\frac{1}{2}})$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{9}{{(x^{2} + 1)}^{\frac{1}{2}}})$