Simplify/Condense 3 natural log of 6x+ natural log of 4y

$3 \ln (6 x) + \ln (4 y)$

Step 1

Simplify each term.

Simplify $3 \ln (6 x)$ by moving $3$ inside the logarithm.

$\ln ({(6 x)}^{3}) + \ln (4 y)$

Apply the product rule to $6 x$ .

$\ln (6^{3} x^{3}) + \ln (4 y)$

Raise $6$ to the power of $3$ .

$\ln (216 x^{3}) + \ln (4 y)$

Step 2

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

$\ln (216 x^{3} (4 y))$

Step 3

Rewrite using the commutative property of multiplication.

$\ln (216 \cdot 4 x^{3} y)$

Step 4

Multiply $216$ by $4$ .

$\ln (864 x^{3} y)$