Precalculus Examples

$\ln (\frac{292}{760})$

Step 1

Rewrite $\ln (\frac{292}{760})$ as $\ln (292) - \ln (760)$ .

$\ln (292) - \ln (760)$

Step 2

Rewrite $\ln (760)$ as $\ln (2^{3} \cdot 5 \cdot 19)$ .

$\ln (292) - \ln (2^{3} \cdot 5 \cdot 19)$

Step 3

Rewrite $\ln (2^{3} \cdot 5 \cdot 19)$ as $\ln (2^{3} \cdot 5) + \ln (19)$ .

$\ln (292) - (\ln (2^{3} \cdot 5) + \ln (19))$

Step 4

Raise $2$ to the power of $3$ .

$\ln (292) - (\ln (8 \cdot 5) + \ln (19))$

Step 5

Multiply $8$ by $5$ .

$\ln (292) - (\ln (40) + \ln (19))$

Step 6

Simplify each term.

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Step 6.1

Rewrite $\ln (40)$ as $\ln (2^{3} \cdot 5)$ .

$\ln (292) - (\ln (2^{3} \cdot 5) + \ln (19))$

Step 6.2

Rewrite $\ln (2^{3} \cdot 5)$ as $\ln (2^{3}) + \ln (5)$ .

$\ln (292) - (\ln (2^{3}) + \ln (5) + \ln (19))$

Step 6.3

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$\ln (292) - (3 \ln (2) + \ln (5) + \ln (19))$

Step 7

Apply the distributive property.

$\ln (292) - (3 \ln (2)) - \ln (5) - \ln (19)$

Step 8

Multiply $3$ by $- 1$ .

$\ln (292) - 3 \ln (2) - \ln (5) - \ln (19)$

Step 9

Simplify each term.

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Step 9.1

Rewrite $\ln (292)$ as $\ln (2^{2} \cdot 73)$ .

$\ln (2^{2} \cdot 73) - 3 \ln (2) - \ln (5) - \ln (19)$

Step 9.2

Rewrite $\ln (2^{2} \cdot 73)$ as $\ln (2^{2}) + \ln (73)$ .

$\ln (2^{2}) + \ln (73) - 3 \ln (2) - \ln (5) - \ln (19)$

Step 9.3

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

$2 \ln (2) + \ln (73) - 3 \ln (2) - \ln (5) - \ln (19)$

Step 10

Subtract $3 \ln (2)$ from $2 \ln (2)$ .

$\ln (73) - \ln (2) - \ln (5) - \ln (19)$