`log_(b^(n))^(a^(m))=K*log_(b)^(a)` where K is

The value of log_(b)a+log_(b^(2))a^(2) + log_(b^(3))a^(3) + ... + log_(b^(n))a^(n)

If (log_(a)N)/(log_(c)N)=(log_(a)N-log_(b)N)/(log_(b)N-log_(c)N), where N>0 and N!=1,a,b,c>0 and not equal to 1, then prove that b^(2)=ac

If log_(b)(n)=2 and log_(n)(2b)=2, then b is equal to

If a^(x) = b , b^(y) = c, c^(z) = a, x = log_(b) a^(k_(1)) , y = log_(c)b^(k_(2)), z = log _(a) c^(k_(3)), , then find K_(1) K_(2) K_(3) .

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

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 =

For positive numbers a,k,T and S where neither a nor Sequals unity,if (log_(s)a)(a^(log_(a)k))=1-log_(s)a*log_(a)T then S equals to

For positive numbers a,k,T and S where neither a nor S equals unity,if (log_(s)a)(a^(log_(a)k))=1-log_(s)a*log_(a)T then S equals to

If log_(b)2=a and log_(b)5=c ,where b>0 with b!=1 , then log_(b)500 is equal to which of the following