Simplify/Condense 5 natural log of 2+7 natural log of x+4 natural log of y

$5 \ln (2) + 7 \ln (x) + 4 \ln (y)$

Step 1

Simplify each term.

Simplify $5 \ln (2)$ by moving $5$ inside the logarithm.

$\ln (2^{5}) + 7 \ln (x) + 4 \ln (y)$

Raise $2$ to the power of $5$ .

$\ln (32) + 7 \ln (x) + 4 \ln (y)$

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

$\ln (32) + \ln (x^{7}) + 4 \ln (y)$

Simplify $4 \ln (y)$ by moving $4$ inside the logarithm.

$\ln (32) + \ln (x^{7}) + \ln (y^{4})$

Step 2

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

$\ln (32 x^{7}) + \ln (y^{4})$

Step 3

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

$\ln (32 x^{7} y^{4})$