Precalculus Examples

$\ln (a + b) + 2 \ln (a - b) - \frac{\ln (c)}{\ln (5)}$

Step 1

Simplify $2 \ln (a - b)$ by moving $2$ inside the logarithm.

$\ln (a + b) + \ln ({(a - b)}^{2}) - \frac{\ln (c)}{\ln (5)}$

Step 2

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

$\ln ((a + b) {(a - b)}^{2}) - \frac{\ln (c)}{\ln (5)}$

Step 3

Apply the distributive property.

$\ln (a {(a - b)}^{2} + b {(a - b)}^{2}) - \frac{\ln (c)}{\ln (5)}$

Step 4

To write $\ln (a {(a - b)}^{2} + b {(a - b)}^{2})$ as a fraction with a common denominator, multiply by $\frac{\ln (5)}{\ln (5)}$ .

$\frac{\ln (a {(a - b)}^{2} + b {(a - b)}^{2}) \ln (5)}{\ln (5)} - \frac{\ln (c)}{\ln (5)}$

Step 5

Combine the numerators over the common denominator.

$\frac{\ln (a {(a - b)}^{2} + b {(a - b)}^{2}) \ln (5) - \ln (c)}{\ln (5)}$