Precalculus Examples

$\frac{\ln (\frac{1600}{1000})}{4}$

Step 1

Cancel the common factor of $1600$ and $1000$ .

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Step 1.1

Factor $200$ out of $1600$ .

$\frac{\ln (\frac{200 (8)}{1000})}{4}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $200$ out of $1000$ .

$\frac{\ln (\frac{200 \cdot 8}{200 \cdot 5})}{4}$

Step 1.2.2

Cancel the common factor.

$\frac{\ln (\frac{200 \cdot 8}{200 \cdot 5})}{4}$

Step 1.2.3

Rewrite the expression.

$\frac{\ln (\frac{8}{5})}{4}$

Step 2

Rewrite $\frac{\ln (\frac{8}{5})}{4}$ as $\frac{1}{4} \ln (\frac{8}{5})$ .

$\frac{1}{4} \ln (\frac{8}{5})$

Step 3

Simplify $\frac{1}{4} \ln (\frac{8}{5})$ by moving $\frac{1}{4}$ inside the logarithm.

$\ln ({(\frac{8}{5})}^{\frac{1}{4}})$

Step 4

Apply the product rule to $\frac{8}{5}$ .

$\ln (\frac{8^{\frac{1}{4}}}{5^{\frac{1}{4}}})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{8^{\frac{1}{4}}}{5^{\frac{1}{4}}})$

Decimal Form:

$0.11750090 \dots$