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

If "log"_(y) x = "log"_(z)y = "log"_(x)z , then

for x,x,z gt 0 Prove that |{:(1,,log_(x)y,,log_(x)z),(log_(y)x,,1,,log_(y)z),(log_(z) x,,log_(z)y,,1):}| =0

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

Solve for x, y , z . log_2 x + log_4 y + log_4 z =2 log_3 y + log_9 z + log_9 x =2 log_4 z + log_16 x + log_16 y =2

For relation 2 log y - log x - log ( y-1) =0

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)]|

The value of x^("log"_(x) a xx "log"_(a)y xx "log"_(y) z) is

The numbers 1/3, 1/3 log _(x) y, 1/3 log _(y) z, 1/7 log _(x) x are in H.P. If y= x ^® and z =x ^(s ), then 4 (r +s)=

Given x = log_(10)12, y = log_(4)2 xx log_(10)9 and z = log_(10) 0.4 , find : (i) x - y - z (ii) 13^(x - y - z)

(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) .