Precalculus Examples

$\ln (\frac{1}{2}) = 21 k$

Step 1

Rewrite the equation as $21 k = \ln (\frac{1}{2})$ .

$21 k = \ln (\frac{1}{2})$

Step 2

Divide each term in $21 k = \ln (\frac{1}{2})$ by $21$ and simplify.

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Step 2.1

Divide each term in $21 k = \ln (\frac{1}{2})$ by $21$ .

$\frac{21 k}{21} = \frac{\ln (\frac{1}{2})}{21}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $21$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{21 k}{21} = \frac{\ln (\frac{1}{2})}{21}$

Step 2.2.1.2

Divide $k$ by $1$ .

$k = \frac{\ln (\frac{1}{2})}{21}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Rewrite $\frac{\ln (\frac{1}{2})}{21}$ as $\frac{1}{21} \ln (\frac{1}{2})$ .

$k = \frac{1}{21} \ln (\frac{1}{2})$

Step 2.3.2

Simplify $\frac{1}{21} \ln (\frac{1}{2})$ by moving $\frac{1}{21}$ inside the logarithm.

$k = \ln ({(\frac{1}{2})}^{\frac{1}{21}})$

Step 2.3.3

Apply the product rule to $\frac{1}{2}$ .

$k = \ln (\frac{1^{\frac{1}{21}}}{2^{\frac{1}{21}}})$

Step 2.3.4

One to any power is one.

$k = \ln (\frac{1}{2^{\frac{1}{21}}})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$k = \ln (\frac{1}{2^{\frac{1}{21}}})$

Decimal Form:

$k = - 0.03300700 \dots$