Precalculus Examples

$2 \log (3) \cdot 4 + 3 \log (3) \cdot 2$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $2 \log (3)$ by moving $2$ inside the logarithm.

$\log (3^{2}) \cdot 4 + 3 \log (3) \cdot 2$

Step 1.2

Raise $3$ to the power of $2$ .

$\log (9) \cdot 4 + 3 \log (3) \cdot 2$

Step 1.3

Multiply $\log (9) \cdot 4$ .

Tap for more steps...

Step 1.3.1

Reorder $\log (9)$ and $4$ .

$4 \cdot \log (9) + 3 \log (3) \cdot 2$

Step 1.3.2

Simplify $4 \cdot \log (9)$ by moving $4$ inside the logarithm.

$\log (9^{4}) + 3 \log (3) \cdot 2$

Step 1.4

Raise $9$ to the power of $4$ .

$\log (6561) + 3 \log (3) \cdot 2$

Step 1.5

Simplify $3 \log (3)$ by moving $3$ inside the logarithm.

$\log (6561) + \log (3^{3}) \cdot 2$

Step 1.6

Raise $3$ to the power of $3$ .

$\log (6561) + \log (27) \cdot 2$

Step 1.7

Multiply $\log (27) \cdot 2$ .

Tap for more steps...

Step 1.7.1

Reorder $\log (27)$ and $2$ .

$\log (6561) + 2 \cdot \log (27)$

Step 1.7.2

Simplify $2 \cdot \log (27)$ by moving $2$ inside the logarithm.

$\log (6561) + \log (27^{2})$

Step 1.8

Raise $27$ to the power of $2$ .

$\log (6561) + \log (729)$

Step 2

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

$\log (6561 \cdot 729)$

Step 3

Multiply $6561$ by $729$ .

$\log (4782969)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (4782969)$

Decimal Form:

$6.67969756 \dots$