Properties of logarithmic function Property (1) log_a 1=0 (2) log_a a=1 (3) log_a (xy)=log_a|x|+log_a|y| (4) log_a(x/y)=log_a |x|-log_a |y|`

Properties of logarithmic function Property (5)log_(a)(x^(n))=n log_(a)|x|(6)log_(a)^(n)x^(m)=(m)/(n)log_(a)x(7)x^(log_(a)y)=y^(log_(a)x)

1+log_(x)y=log_(2)y

Prove that log_(a)xy=log_(a)x+log_(a)y.

Properties of logarithmic function Property (8) If a>1 then the values of f(x)=log_a x increases with an increase in x ie xlty hArr log_a x lt log_a y (9) If 0

|(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)|=

log_(2)(log_(2)(log_(3)x))=log_(2)(log_(2)(log_(2)y))=0 find (x+y)=?

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 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)]|

If log_(2)(log_(2)(log_(3)x))=log_(3)(log_(3)(log_(2)y))=0 , then x-y is equal to :