Precalculus Examples

$\log (2000) - \log (40) - \log (2)$

Step 1

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

$\log (\frac{2000}{40}) - \log (2)$

Step 2

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

$\log (\frac{\frac{2000}{40}}{2})$

Step 3

Cancel the common factor of $2000$ and $40$ .

Tap for more steps...

Step 3.1

Factor $40$ out of $2000$ .

$\log (\frac{\frac{40 \cdot 50}{40}}{2})$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $40$ out of $40$ .

$\log (\frac{\frac{40 \cdot 50}{40 (1)}}{2})$

Step 3.2.2

Cancel the common factor.

$\log (\frac{\frac{40 \cdot 50}{40 \cdot 1}}{2})$

Step 3.2.3

Rewrite the expression.

$\log (\frac{\frac{50}{1}}{2})$

Step 3.2.4

Divide $50$ by $1$ .

$\log (\frac{50}{2})$

Step 4

Cancel the common factor of $50$ and $2$ .

Tap for more steps...

Step 4.1

Factor $2$ out of $50$ .

$\log (\frac{2 \cdot 25}{2})$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $2$ out of $2$ .

$\log (\frac{2 \cdot 25}{2 (1)})$

Step 4.2.2

Cancel the common factor.

$\log (\frac{2 \cdot 25}{2 \cdot 1})$

Step 4.2.3

Rewrite the expression.

$\log (\frac{25}{1})$

Step 4.2.4

Divide $25$ by $1$ .

$\log (25)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (25)$

Decimal Form:

$1.39794000 \dots$