Simplify/Condense 3 log of 7+ log of 2

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

Simplify each term.

Simplify $3 \log (7)$ by moving $3$ inside the logarithm.

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

Raise $7$ to the power of $3$ .

$\log (343) + \log (2)$

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

$\log (343 \cdot 2)$

Multiply $343$ by $2$ .

$\log (686)$

The result can be shown in multiple forms.

Exact Form:

$\log (686)$

Decimal Form:

$2.83632411 \dots$