If `m,n,agt0; a!=1 ; log_a (m^n)=nlog_a m `

If m;n;a>0;a!=1;log_(a)(m^(n))=n log_(a)m

_m^( If );n;a>0;a!=1;log_(a)(mn)=log_(a)m+log_(a)n

m;n;a>0;a!=1;log_(a)((m)/(n))=log_(a)m-log_(a)n

log(x)^(n)=n.log x is true for

Let m,n be two positive real numbers and define f(n)=int_(0)^(oo)x^(n-1)e^(-x)dx and g(m,n)=int_(0)^(1)x^(m-1)(1-m)^(n-1)dx . It is known that f(n) for n gt 0 is finite and g(m, n) = g(n, m) for m, n gt 0. int_(0)^(1)x^(m)(log_(e).(1)/(x))dx=