Find `log (x^2/y^2) +log(y^2/z^2)+ log (z^2/x^2)` =?

The value of the determinant |[log_a(x/y), log_a(y/z), log_a(z/x)], [log_b (y/z), log_b (z/x), log_b (x/y)], [log_c (z/x), log_c (x/y), log_c (y/z)]|

Find (d^2y)/(dx^2) , where y=log((x^2)/(e^2)) .

For the system of equation "log"_(10) (x^(3)-x^(2)) = "log"_(5)y^(2) "log"_(10)(y^(3)-y^(2)) = "log"_(5) z^(2) "log"_(10)(z^(3)-z^(2)) = "log"_(5)x^(2) Which of the following is/are true?

(i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the value of (1)/(x) + (1)/(y) + (1)/(z) " is " (5)/(3) . If a, x, y, z b are in HP, then find a and b (ii) If x,y,z are in HP, then show that log (x +z) + log (x +z -2y) = 2 log ( x -z) .

The number of ordered pairs (x, y) satisfying 4("log"_(2) x^(2))^(2) + 1 = 2 "log"_(2)y " and log"_(2)x^(2) ge "log"_(2) y , is

Prove that : log _ y^(x) . log _z^(y) . log _a^(z) = log _a ^(x)

If ("log"3)/(x-y) = ("log"5)/(y-z) = ("log" 7)/(z-x), " then " 3^(x+y) 5^(y+z) 7^(z+x) =

STATEMENT-1 : If log (x + z) + log (x -2y +z) = 2 log (x -z) then x,y,z are in H.P. STATEMENT-2 : If p , q , r in AP and (a -x)/(px) = (a-y)/(qy) = (a-z)/(rz) , then x, y, z are in A.P. STATEMENT-3 : If (a + b)/(1 - ab), b, (b + c)/(1 - bc) are in A .P. then a, (1)/(b) , c are in H.P.

If log xy^(3) = m and log x ^(3) y ^(2) = p, " find " log (x^(2) -: y) in terms of m and p.

Given : (log x)/(log y) = (3)/(2) and log(xy) = 5, find the values of x and y.