Simplify/Condense log of 4- log of 10

$\log (4) - \log (10)$

Step 1

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

$\log (\frac{4}{10})$

Step 2

Cancel the common factor of $4$ and $10$ .

Factor $2$ out of $4$ .

$\log (\frac{2 (2)}{10})$

Cancel the common factors.

Factor $2$ out of $10$ .

$\log (\frac{2 \cdot 2}{2 \cdot 5})$

Cancel the common factor.

$\log (\frac{2 \cdot 2}{2 \cdot 5})$

Rewrite the expression.

$\log (\frac{2}{5})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{2}{5})$

Decimal Form:

$- 0.39794000 \dots$