Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Apply the product rule to $6 x$ .

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

Step 1.3

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 $4$ .

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