Evaluate log of 8+ log of 10- log of 2

$\log (8) + \log (10) - \log (2)$

Step 1

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

$\log (8 \cdot 10) - \log (2)$

Step 2

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

$\log (\frac{8 \cdot 10}{2})$

Step 3

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 \cdot 10$ .

$\log (\frac{2 (4 \cdot 10)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$\log (\frac{2 (4 \cdot 10)}{2 (1)})$

Cancel the common factor.

$\log (\frac{2 (4 \cdot 10)}{2 \cdot 1})$

Rewrite the expression.

$\log (\frac{4 \cdot 10}{1})$

Divide $4 \cdot 10$ by $1$ .

$\log (4 \cdot 10)$

Step 4

Multiply $4$ by $10$ .

$\log (40)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (40)$

Decimal Form:

$1.60205999 \dots$