Simplify/Condense 2 natural log of x- natural log of 3+ natural log of 6

$2 \ln (x) - \ln (3) + \ln (6)$

Step 1

Simplify $2 \ln (x)$ by moving $2$ inside the logarithm.

$\ln (x^{2}) - \ln (3) + \ln (6)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{x^{2}}{3}) + \ln (6)$

Step 3

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

$\ln (\frac{x^{2}}{3} \cdot 6)$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\ln (\frac{x^{2}}{3} \cdot (3 (2)))$

Cancel the common factor.

$\ln (\frac{x^{2}}{3} \cdot (3 \cdot 2))$

Rewrite the expression.

$\ln (x^{2} \cdot 2)$

Step 5

Move $2$ to the left of $x^{2}$ .

$\ln (2 x^{2})$