Calculus Examples

$\ln (\frac{3125}{4}) - 3$

Step 1

Rewrite $\ln (\frac{3125}{4})$ as $\ln (3125) - \ln (4)$ .

$\ln (3125) - \ln (4) - 3$

Step 2

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\ln (3125) - \ln (2^{2}) - 3$

Step 3

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$\ln (3125) - (2 \ln (2)) - 3$

Step 4

Multiply $2$ by $- 1$ .

$\ln (3125) - 2 \ln (2) - 3$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\ln (3125)$ as $\ln (5^{5})$ .

$\ln (5^{5}) - 2 \ln (2) - 3$

Step 5.2

Expand $\ln (5^{5})$ by moving $5$ outside the logarithm.

$5 \ln (5) - 2 \ln (2) - 3$