Solve for k natural log of 1/2=23k

$\ln (\frac{1}{2}) = 23 k$

Rewrite the equation as $23 k = \ln (\frac{1}{2})$ .

$23 k = \ln (\frac{1}{2})$

Divide each term in $23 k = \ln (\frac{1}{2})$ by $23$ and simplify.

Divide each term in $23 k = \ln (\frac{1}{2})$ by $23$ .

$\frac{23 k}{23} = \frac{\ln (\frac{1}{2})}{23}$

Simplify the left side.

Cancel the common factor of $23$ .

Cancel the common factor.

$\frac{23 k}{23} = \frac{\ln (\frac{1}{2})}{23}$

Divide $k$ by $1$ .

$k = \frac{\ln (\frac{1}{2})}{23}$

Simplify the right side.

Rewrite $\frac{\ln (\frac{1}{2})}{23}$ as $\frac{1}{23} \ln (\frac{1}{2})$ .

$k = \frac{1}{23} \ln (\frac{1}{2})$

Simplify $\frac{1}{23} \ln (\frac{1}{2})$ by moving $\frac{1}{23}$ inside the logarithm.

$k = \ln ({(\frac{1}{2})}^{\frac{1}{23}})$

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

$k = \ln (\frac{1^{\frac{1}{23}}}{2^{\frac{1}{23}}})$

One to any power is one.

$k = \ln (\frac{1}{2^{\frac{1}{23}}})$

The result can be shown in multiple forms.

Exact Form:

$k = \ln (\frac{1}{2^{\frac{1}{23}}})$

Decimal Form:

$k = - 0.03013683 \dots$