Find the log of? Z=5.2e^0.866

Jun 12, 2018

$\ln Z = \ln 5.2 + 0.866$

Explanation:

We have to

$Z = 5.2 {e}^{0.866}$

To find $\ln Z$, we must apply a few properties of logarithms. If $a$, $c$ and $b$ are real positive numbers, $b \ne 1$, then

${\log}_{b} \left(a c\right) = {\log}_{b} a + {\log}_{b} c$
${\log}_{b} {b}^{a} = a$

Hence,

$\ln Z = \ln \left(5.2 {e}^{0.866}\right) = \ln 5.2 + \ln \left({e}^{0.866}\right) = \ln 5.2 + 0.866$