If `log_(4)10=x,log_(2)20=y andlog_(5)8=z`.prove that `1/(x+1)+1/(y+1)+1/(z+1)=1.`

if x =log_a (bc), y= log_b (ca) and z=log_c(ab) then 1/(x+1)+1/(y+1)+1/(z+1)

If x=log_(2a) a,y=log_(3a) 2a and z=log_(4a) 3a then prove that xyz+1=2yz

If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

If log_(a)5=x and log_(a)7=y , then log_(a)sqrt(1,4)=

If x=log_(2a)((bcd)/2), y=log_(3b)((acd)/3), z=log_(4c)((abd)/4) and w=log_(5d)((abc)/5) and 1/(x+1)+1/(y+1)+1/(z+1)+1/(w+1) = log_(abcd)N+1, then value of N/40 is

If log_(1/3) |z+1| > log_(1/3) |z-1| then prove that Re(z) < 0.

If y=(x-1)log(x-1)-(x+1)log(x+1) , prove that : dy/dx = log((x-1)/(1+x))

If y=(x-1)log(x-1)-(x+1)log(x+1) , prove that (dy)/(dx)=log((x-1)/(1+x))

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............