Precalculus Examples

$\frac{1}{0.3321} \cdot \ln (\frac{35000}{10500})$

Step 1

Divide $1$ by $0.3321$ .

$3.01114122 \cdot \ln (\frac{35000}{10500})$

Step 2

Cancel the common factor of $35000$ and $10500$ .

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Step 2.1

Factor $3500$ out of $35000$ .

$3.01114122 \cdot \ln (\frac{3500 (10)}{10500})$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3500$ out of $10500$ .

$3.01114122 \cdot \ln (\frac{3500 \cdot 10}{3500 \cdot 3})$

Step 2.2.2

Cancel the common factor.

$3.01114122 \cdot \ln (\frac{3500 \cdot 10}{3500 \cdot 3})$

Step 2.2.3

Rewrite the expression.

$3.01114122 \cdot \ln (\frac{10}{3})$

Step 3

Simplify $3.01114122 \ln (\frac{10}{3})$ by moving $3.01114122$ inside the logarithm.

$\ln ({(\frac{10}{3})}^{3.01114122})$

Step 4

Apply the product rule to $\frac{10}{3}$ .

$\ln (\frac{10^{3.01114122}}{3^{3.01114122}})$

Step 5

Raise $10$ to the power of $3.01114122$ .

$\ln (\frac{1025.98549877}{3^{3.01114122}})$

Step 6

Raise $3$ to the power of $3.01114122$ .

$\ln (\frac{1025.98549877}{27.33250764})$

Step 7

Divide $1025.98549877$ by $27.33250764$ .

$\ln (37.53718876)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\ln (37.53718876)$

Decimal Form:

$3.62533214 \dots$