Write as a Single Logarithm 2 log of 4+ log of 2+ log of 2

$2 \log (4) + \log (2) + \log (2)$

Step 1

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

$2 \log (4) + \log (2 \cdot 2)$

Step 2

Simplify each term.

Simplify $2 \log (4)$ by moving $2$ inside the logarithm.

$\log (4^{2}) + \log (2 \cdot 2)$

Raise $4$ to the power of $2$ .

$\log (16) + \log (2 \cdot 2)$

Multiply $2$ by $2$ .

$\log (16) + \log (4)$

Step 3

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

$\log (16 \cdot 4)$

Step 4

Multiply $16$ by $4$ .

$\log (64)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (64)$

Decimal Form:

$1.80617997 \dots$