Precalculus Examples

$6 \log (8) \cdot 11 + 12 \log (8) \cdot 2$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $6 \log (8)$ by moving $6$ inside the logarithm.

$\log (8^{6}) \cdot 11 + 12 \log (8) \cdot 2$

Step 1.2

Raise $8$ to the power of $6$ .

$\log (262144) \cdot 11 + 12 \log (8) \cdot 2$

Step 1.3

Multiply $\log (262144) \cdot 11$ .

Tap for more steps...

Step 1.3.1

Reorder $\log (262144)$ and $11$ .

$11 \cdot \log (262144) + 12 \log (8) \cdot 2$

Step 1.3.2

Simplify $11 \cdot \log (262144)$ by moving $11$ inside the logarithm.

$\log (262144^{11}) + 12 \log (8) \cdot 2$

Step 1.4

Simplify $12 \log (8)$ by moving $12$ inside the logarithm.

$\log (262144^{11}) + \log (8^{12}) \cdot 2$

Step 1.5

Raise $8$ to the power of $12$ .

$\log (262144^{11}) + \log (68719476736) \cdot 2$

Step 1.6

Multiply $\log (68719476736) \cdot 2$ .

Tap for more steps...

Step 1.6.1

Reorder $\log (68719476736)$ and $2$ .

$\log (262144^{11}) + 2 \cdot \log (68719476736)$

Step 1.6.2

Simplify $2 \cdot \log (68719476736)$ by moving $2$ inside the logarithm.

$\log (262144^{11}) + \log (68719476736^{2})$

Step 1.7

Raise $68719476736$ to the power of $2$ .

$\log (262144^{11}) + \log (4722366482869640000000)$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (262144^{11} \cdot 4722366482869640000000)$

Step 3

Move $4722366482869640000000$ to the left of $262144^{11}$ .

$\log (4722366482869640000000 \cdot 262144^{11})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (4722366482869640000000 \cdot 262144^{11})$

Decimal Form:

$81.27809882 \dots$