Precalculus Examples

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

Step 1

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\frac{\ln (2^{2})}{4}$

Step 2

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$\frac{2 \ln (2)}{4}$

Step 3

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $2 \ln (2)$ .

$\frac{2 (\ln (2))}{4}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $4$ .

$\frac{2 \ln (2)}{2 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{2 \ln (2)}{2 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{\ln (2)}{2}$

Step 4

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

$\frac{1}{2} \ln (2)$

Step 5

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

$\ln (2^{\frac{1}{2}})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\ln (2^{\frac{1}{2}})$

Decimal Form:

$0.34657359 \dots$