I need help with this proof...
Prove that $\displaystyle ln 5 sqrt{e} = 1/5$
It is actually like ln e^(1/5) but I dont know how to make the 5 small...
Recall that
$\displaystyle log(n \cdot a) = log(n) + log(a)$
What does $\displaystyle a^b$ mean? It means $\displaystyle a^b = a\cdot a \cdot ~ ... ~ \cdot a$ where we are doing this "b" times.
So
$\displaystyle log(a^b) = log(a) + log(a) + ~ ... ~ + log(a) = b \cdot log(a)$
Note that it does not matter what base the logarithm is to:
$\displaystyle log_{10}(a^b) = b \cdot log_{10}(a)$
and
$\displaystyle log_2(a^b) = b \cdot log_2(a)$
-Dan