# How do you condense log 2 ln 8 +5 ln z?

$\ln \left(\sqrt[\ln 10]{{8}^{\ln} 2} \cdot {z}^{5}\right)$
We know that $\log x = \ln \frac{x}{\ln} 10$ so let's use this.
$\log 2 \ln 8 + 5 \ln z = \ln \frac{2}{\ln} 10 \cdot \ln 8 + \ln {z}^{5} =$
$\ln {8}^{\ln \frac{2}{\ln} 10} + \ln {z}^{5} = \ln \left(\sqrt[\ln 10]{{8}^{\ln} 2} \cdot {z}^{5}\right)$