Question

log of 3squareroot of 5 base 5???

Answer 1

\[\log_{5} 3\sqrt{5}\]?

Answer 2

http://www.wolframalpha.com/input/?i=log5%283*sqrt%285%29%29

Answer 3

=1.1826061944859852951345663592710522530246693998731672096600...

Answer 4

\[\log_{5} 3\sqrt{5} = x \]
apply change of base formula, recall...
\[\log_{A} B = (\log_{10} B )\div(\log_{10}A) \]
a funny analogy is that B is the bigger one right?
so B is the BIG WIFE
A is the base, visually smaller than B the big wife right? :)
A is the concubine,
So when you apply change of base, the big wife will forever be upstairs (bigger) and the concubine will always be below, silly but i hope its funny and helps to remember.

therefore
\[\log_{5} (3\sqrt{5}) = (\log_{10}(3\sqrt{5})) \div (\log_{10}(5)) \]
You change it to base 10 because your calculator can only calculate when it is log base 10 or log base e (ln)

Answer 5

it would be useful to convert into exponential form,
because it is hard to evaluate this :)