Question

Can you show me why logn^2 = 2log2n?

Answer 1

\[\log_{}n ^{2} = 2\log_{2}n \]

Answer 2

its an identity
\[\log (n^{a}) = a \log(n)\]
you could also prove it using product identity
\[\log(n^{2}) = \log(n*n) = \log(n) +\log(n) = 2\log(n)\]

Answer 3

ah ok, but why does the base change from base 10 to base 2?

Answer 4

or I think maybe the 1st one is actually base 2 as well...

Answer 5

umm yeah identities only work with like bases...

Answer 6

log(n^2)

log(n*n)

log(n) + log(n)

2 log(n)

Answer 7

thrms are not accepted on faith ... they are proven or rejected

Answer 8

ok thanks everyone

Answer 9

thanks too amistre

Answer 10

yep :)