`a^(log_(b)(log_(b)N))/(log_(b)a)`

The value of a^(("log"_(b)("log"_(b)x))/("log"_(b) a)) , is

The value of (6 a^(log_(e)b)(log_(a^(2))b)(log_(b^(2))a))/(e^(log_(e)a*log_(e)b)) is

The value of ("log"_(a)("log"_(b)a))/("log"_(b)("log"_(a)b)) , is

The value of a^((log_b(log_bx))/(log_b a)), is

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

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 :

If the equation (log_(12)(log_(8)(log_(4)x)))/(log_(5)(log_(4)(log_(y)(log_(2)x))))=0 has a solution for 'x' when c lt y lt b, y ne a , where 'b' is as large as possible, then the value of (a+b+c) is equals to :

If the equation (log_(12)(log_(8)(log_(4)x)))/(log_(5)(log_(4)(log_(y)(log_(2)x))))=0 has a solution for 'x' when c lt y lt b, y ne a , where 'b' is as large as possible, then the value of (a+b+c) is equals to :

Compute the following a^(((log)_b((log)_a N))/((log)_b\ \ a))

If a,b,c are distinct real number different from 1 such that (log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to