Write as a Single Logarithm 7 log of 2+ log of 3

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

Step 1

Simplify each term.

Simplify $7 \log (2)$ by moving $7$ inside the logarithm.

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

Raise $2$ to the power of $7$ .

$\log (128) + \log (3)$

Step 2

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

$\log (128 \cdot 3)$

Step 3

Multiply $128$ by $3$ .

$\log (384)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (384)$

Decimal Form:

$2.58433122 \dots$