Write as a Single Logarithm 3/4( natural log of a+ natural log of b)

$\frac{3}{4} (\ln (a) + \ln (b))$

Step 1

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

$\frac{3}{4} \cdot \ln (a b)$

Step 2

Simplify $\frac{3}{4} \ln (a b)$ by moving $\frac{3}{4}$ inside the logarithm.

$\ln ({(a b)}^{\frac{3}{4}})$

Step 3

Apply the product rule to $a b$ .

$\ln (a^{\frac{3}{4}} b^{\frac{3}{4}})$