For `a;n gt0` and `a!=1 ; a^(log_a (n))=n`

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

if quad 0,c>0,b=sqrt(ac),a!=1,c!=1,ac!=1 and n>0 then the value of (log a^(n)-log b^(n))/(log b^(n)-log c^(n)) is equal to

( The value of )/(log_(2)N)+(1)/(log_(4)N)+...+(1)/(log_(1988)N) is ;(N>0 and N!=0)( i) (1)/(log_(1998)((1)/(N)))( ii) log_(N)(1998!) (iii) log _(N)1998 (iv) none of these

N=n! , where ngt2 . Find the value of (log_(2)N)^(-1)+(log_(3)N)^(-1)+(log_(4)N)^(-1)+. . . . . (log_(n)N)^(-1) .

if quad 0,c>0,b=sqrt(a)c,a!=1,c!=1,ac!=1a and n>0 then the value of (log_(a)n-log_(b)n)/(log_(b)n-log_(c)n) is equal to

If a gt 0, c gt 0 , " b " = sqrt(ac) and " ac " ne 1 , N gt 0 , then (log_(a) N - log_(b) N)/(log_(b) N - log_(c) N) =

Suppose a,b,c gt 1 and n in N, n ge 2 . If log_(a)(n),log_(b)(n),log_(c )(n) are in A.P., then log_(a)b+log_(c )b =

Two sequences lta_(n)gtandltb_(n)gt are defined by a_(n)=log((5^(n+1))/(3^(n-1))),b_(n)={log((5)/(3))}^(n) , then