Precalculus Examples

$\ln (8 + 2) \ln (2)$

Step 1

Add $8$ and $2$ .

$\ln (10) \ln (2)$

Step 2

Rewrite $\ln (10)$ as $\ln (2 (5))$ .

$\ln (2 (5)) \ln (2)$

Step 3

Rewrite $\ln (2 (5))$ as $\ln (2) + \ln (5)$ .

$(\ln (2) + \ln (5)) \ln (2)$

Step 4

Apply the distributive property.

$\ln (2) \ln (2) + \ln (5) \ln (2)$

Step 5

Multiply $\ln (2) \ln (2)$ .

Tap for more steps...

Step 5.1

Raise $\ln (2)$ to the power of $1$ .

$\ln^{1} (2) \ln (2) + \ln (5) \ln (2)$

Step 5.2

Raise $\ln (2)$ to the power of $1$ .

$\ln^{1} (2) \ln^{1} (2) + \ln (5) \ln (2)$

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\ln (2)}^{1 + 1} + \ln (5) \ln (2)$

Step 5.4

Add $1$ and $1$ .

$\ln^{2} (2) + \ln (5) \ln (2)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\ln^{2} (2) + \ln (5) \ln (2)$

Decimal Form:

$1.59603036 \dots$