`log_(b^3) (a^5) log_(c^2) (b^5) log_(a^4) (c^5)`=

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 :

Write each of the following as single logarithm: (a) 1+ log_(2) 5" "(b) 2- log_(3) 7 (c) 2log_(10) x+3 log_(10) y - 5 log_(10) z

If log_(a)b+log_(b)c+log_(c)a vanishes where a, b and c are positive reals different from unity then the value of (log_(a)b)^(3) + (log_(b)c)^(3) + (log_(c)a)^(3) is

If log_(a)b+log_(b)c+log_(c)a vanishes where a, b and c are positive reals different than unity then the value of (log_(a)b)^(3) + (log_(b)c)^(3) + (log_(c)a)^(3) is

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

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

If "log"_(2) a + "log"_(4) b + "log"_(4) c = 2 "log"_(9) a + "log"_(3) b + "log"_(9) c = 2 "log"_(16) a + "log"_(16) b + "log"_(4) c =2 , then

Arrange log_(2) 5, log_(0.5) 5, log_(7) 5, log_(3) 5 in decreasing order.

Evaluate : (i) log_(b)a xx log_(c)b xx log_(a)c (ii) log_(3) 8 div log_(9) 16 (iii) (log_(5)8)/(log_(25)16 xx log_(100)10)

Which of the following numbers are non positive? (A) 5^(log_(11)7)-7(log_(11)5) (B) log_(3)(sqrt(7)-2) (C) log_(7)((1)/(2))^(-1//2) (D) log_(sqrt(2)-1) (sqrt(2)+1)/(sqrt(2)-1)