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

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

Show that the sequence loga ,log((a^2)/b),log((a^3)/(b^2)),log((a^4)/(b^3)), forms an A.P.

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

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 3^(x) = 4^(x-1) , then x = a. (2 log_(3) 2)/(2log_(3) 2-1) b. 2/(2-log_(2)3) c. 1/(1-log_(4)3) d. (2 log_(2)3)/(2 log_(2) 3-1)

Statement-1: If a =y^(2), b=z^(2) " and " c= x^(2), " then log"_(a) x^(3) xx "log"_(b) y^(3) xx "log"_(c)z^(3) = (27)/(8) Statement-2: "log"_(b) a = (1)/("log"_(a)b)

int_0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a) log(2/3) (b) log(3/2) (c) log(3/4) (d) log(4/3)

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) .

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)