Precalculus Examples

$\ln (\frac{1}{2}) = 19 k$

Step 1

Rewrite the equation as $19 k = \ln (\frac{1}{2})$ .

$19 k = \ln (\frac{1}{2})$

Step 2

Divide each term in $19 k = \ln (\frac{1}{2})$ by $19$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $19 k = \ln (\frac{1}{2})$ by $19$ .

$\frac{19 k}{19} = \frac{\ln (\frac{1}{2})}{19}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $19$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{19 k}{19} = \frac{\ln (\frac{1}{2})}{19}$

Step 2.2.1.2

Divide $k$ by $1$ .

$k = \frac{\ln (\frac{1}{2})}{19}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Rewrite $\frac{\ln (\frac{1}{2})}{19}$ as $\frac{1}{19} \ln (\frac{1}{2})$ .

$k = \frac{1}{19} \ln (\frac{1}{2})$

Step 2.3.2

Simplify $\frac{1}{19} \ln (\frac{1}{2})$ by moving $\frac{1}{19}$ inside the logarithm.

$k = \ln ({(\frac{1}{2})}^{\frac{1}{19}})$

Step 2.3.3

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

$k = \ln (\frac{1^{\frac{1}{19}}}{2^{\frac{1}{19}}})$

Step 2.3.4

One to any power is one.

$k = \ln (\frac{1}{2^{\frac{1}{19}}})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$k = \ln (\frac{1}{2^{\frac{1}{19}}})$

Decimal Form:

$k = - 0.03648143 \dots$