Precalculus Examples

$\ln (\frac{5}{6 x^{6} y})$

Step 1

Rewrite $\ln (\frac{5}{6 x^{6} y})$ as $\ln (5) - \ln (6 x^{6} y)$ .

$\ln (5) - \ln (6 x^{6} y)$

Step 2

Rewrite $\ln (6 x^{6} y)$ as $\ln (6 x^{6}) + \ln (y)$ .

$\ln (5) - (\ln (6 x^{6}) + \ln (y))$

Step 3

Rewrite $\ln (6 x^{6})$ as $\ln (6) + \ln (x^{6})$ .

$\ln (5) - (\ln (6) + \ln (x^{6}) + \ln (y))$

Step 4

Expand $\ln (x^{6})$ by moving $6$ outside the logarithm.

$\ln (5) - (\ln (6) + 6 \ln (x) + \ln (y))$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

$\ln (5) - (\ln (2 (3)) + 6 \ln (x) + \ln (y))$

Step 5.1.2

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

$\ln (5) - (\ln (2) + \ln (3) + 6 \ln (x) + \ln (y))$

Step 5.2

Apply the distributive property.

$\ln (5) - \ln (2) - \ln (3) - (6 \ln (x)) - \ln (y)$

Step 5.3

Multiply $6$ by $- 1$ .

$\ln (5) - \ln (2) - \ln (3) - 6 \ln (x) - \ln (y)$