# How do you convert 1/3ln(x) - 3 ln (4) - 5 ln(z) into a single logarithm?

Nov 13, 2015

$\ln \left({x}^{\frac{1}{3}} \cdot \frac{1}{64 {z}^{5}}\right)$

#### Explanation:

$a \ln b = \ln {b}^{a}$

$\ln a + \ln b = \ln \left(a b\right)$

Expression = $E = \ln \left({x}^{\frac{1}{3}}\right) + \ln {4}^{- 3} + \ln {z}^{- 5}$

$E = \ln \left({x}^{\frac{1}{3}} \cdot {4}^{- 3} \cdot {z}^{- 5}\right)$