Precalculus Examples

$\log (2) \cdot 7 + \log (4) \cdot 3$

Simplify each term.

Tap for more steps...

Multiply $\log (2) \cdot 7$ .

Tap for more steps...

Reorder $\log (2)$ and $7$ .

$7 \cdot \log (2) + \log (4) \cdot 3$

Simplify $7 \cdot \log (2)$ by moving $7$ inside the logarithm.

$\log (2^{7}) + \log (4) \cdot 3$

Raise $2$ to the power of $7$ .

$\log (128) + \log (4) \cdot 3$

Multiply $\log (4) \cdot 3$ .

Tap for more steps...

Reorder $\log (4)$ and $3$ .

$\log (128) + 3 \cdot \log (4)$

Simplify $3 \cdot \log (4)$ by moving $3$ inside the logarithm.

$\log (128) + \log (4^{3})$

Raise $4$ to the power of $3$ .

$\log (128) + \log (64)$

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

$\log (128 \cdot 64)$

Multiply $128$ by $64$ .

$\log (8192)$

The result can be shown in multiple forms.

Exact Form:

$\log (8192)$

Decimal Form:

$3.91338994 \dots$