Precalculus Examples

$\log_{2} (56 \cdot \sqrt{2}) - (\log_{2} ({(7)}^{2}) + 1 - \log_{2} (49))$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{2} (56 \sqrt{2}) - (\log_{2} (\frac{{(7)}^{2}}{49}) + 1)$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

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

$\log_{2} (56 \sqrt{2}) - (\log_{2} (\frac{49}{49}) + 1)$

Step 2.2

Divide $49$ by $49$ .

$\log_{2} (56 \sqrt{2}) - (\log_{2} (1) + 1)$

Step 2.3

Logarithm base $2$ of $1$ is $0$ .

$\log_{2} (56 \sqrt{2}) - (0 + 1)$

Step 3

Add $0$ and $1$ .

$\log_{2} (56 \sqrt{2}) - 1 \cdot 1$

Step 4

Multiply $- 1$ by $1$ .

$\log_{2} (56 \sqrt{2}) - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{2} (56 \sqrt{2}) - 1$

Decimal Form:

$5.30735492 \dots$