Calculus Examples

$\ln (\frac{6 y}{5 z})$

Step 1

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

$\ln (6 y) - \ln (5 z)$

Step 2

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

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

Step 3

Rewrite $\ln (5 z)$ as $\ln (5) + \ln (z)$ .

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

Step 4

Simplify each term.

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Step 4.1

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

$\ln (2 (3)) + \ln (y) - (\ln (5) + \ln (z))$

Step 4.2

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

$\ln (2) + \ln (3) + \ln (y) - (\ln (5) + \ln (z))$

Step 4.3

Apply the distributive property.

$\ln (2) + \ln (3) + \ln (y) - \ln (5) - \ln (z)$