Answer
$0$
Work Step by Step
RECALL:
(i) $\log_b{b}=1.$
(ii) $\log_b{b^x}=x.$
(iii) $\log_b{1} = 0.$
(iv) $\ln{x} = \log_e{x}.$
(v) $\log{x} = \log_{10}{x}.$
Use rule (iv) above to obtain:
$\log{(\ln{e})}=\log{(\log_e{e})}.$
Use rule (i) above to obtain
$\log{(\log_e{e})}=\log{1}.$
Use rule (v) to obtain
$\log{1}=\log_{10}{1}.$
Use rule (iii) above to obtain
$\log_{10}{1} = 0.$
Therefore $\log{(\ln{e})}=0$.
