Write as a Single Logarithm natural log of k+2 natural log of 7r

$\ln (k) + 2 \ln (7 r)$

Step 1

Simplify each term.

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

$\ln (k) + \ln ({(7 r)}^{2})$

Apply the product rule to $7 r$ .

$\ln (k) + \ln (7^{2} r^{2})$

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

$\ln (k) + \ln (49 r^{2})$

Step 2

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

$\ln (k (49 r^{2}))$

Step 3

Rewrite using the commutative property of multiplication.

$\ln (49 k r^{2})$