Calculus Examples

$\ln (\frac{7 y}{6 z})$

Step 1

Rewrite $\ln (\frac{7 y}{6 z})$ as $\ln (7 y) - \ln (6 z)$ .

$\ln (7 y) - \ln (6 z)$

Step 2

Rewrite $\ln (7 y)$ as $\ln (7) + \ln (y)$ .

$\ln (7) + \ln (y) - \ln (6 z)$

Step 3

Rewrite $\ln (6 z)$ as $\ln (6) + \ln (z)$ .

$\ln (7) + \ln (y) - (\ln (6) + \ln (z))$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

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

$\ln (7) + \ln (y) - (\ln (2 (3)) + \ln (z))$

Step 4.1.2

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

$\ln (7) + \ln (y) - (\ln (2) + \ln (3) + \ln (z))$

Step 4.2

Apply the distributive property.

$\ln (7) + \ln (y) - \ln (2) - \ln (3) - \ln (z)$