Precalculus Examples

$\log (x) + \log (x^{2} + 1) - \log (7) - \log (x + 1)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x (x^{2} + 1)) - \log (7) - \log (x + 1)$

Step 2

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

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

Step 3

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

$\log (\frac{\frac{x (x^{2} + 1)}{7}}{x + 1})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log (\frac{x (x^{2} + 1)}{7} \cdot \frac{1}{x + 1})$

Step 5

Multiply $\frac{x (x^{2} + 1)}{7}$ by $\frac{1}{x + 1}$ .

$\log (\frac{x (x^{2} + 1)}{7 (x + 1)})$