Expand the Logarithmic Expression log base x of 3m(4n)

$\log_{x} (3 m) (4 n)$

Step 1

Rewrite $\log_{x} (3 m)$ as $\log_{x} (3) + \log_{x} (m)$ .

$(\log_{x} (3) + \log_{x} (m)) (4 n)$

Step 2

Apply the distributive property.

$\log_{x} (3) (4 n) + \log_{x} (m) (4 n)$

Step 3

Rewrite using the commutative property of multiplication.

$4 \log_{x} (3) n + \log_{x} (m) (4 n)$

Step 4

Rewrite using the commutative property of multiplication.

$4 \log_{x} (3) n + 4 \log_{x} (m) n$

Step 5

Reorder factors in $4 \log_{x} (3) n + 4 \log_{x} (m) n$ .

$4 n \log_{x} (3) + 4 n \log_{x} (m)$