`log_((x+6)/3)(log_2[(x-1)/(x+2)])>0`

log_(2)(x+1)-log_(2)(3x-1)=2

log_(7)((2x-6)/(2x-1))>0

log_(2)log_(3)log_(4)(x-1)>0

Solve for x, (a) (log_(10)(x-3))/(log_(10)(x^(2)-21))=(1)/(2),(b)log(log x)+log(log x^(3)-2)=0; where base of log is 10 everywhere.

log_((1)/(2))log_(3)(x^(2)+5)+1<=0

The domain of definition of f(x)=log_(0.5){-log_(2)((3x-1)/(3x+2))} , is

The domain of definition of f(x)=log_(0.5){-log_(2)((3x-1)/(3x+2))} , is

4^(log_(10)x+1)-6^(log_(10)x)-2*3^(log_(10)x^(2)+2)=0. Find x

Solve the following equations : (i) log_(x)(4x-3)=2 (ii) log_2(x-1)+log_(2)(x-3)=3 (iii) log_(2)(log_(8)(x^(2)-1))=0 (iv) 4^(log_(2)x)-2x-3=0

Consider the inequalities log_(5)(x-3)+(1)/(2)log_(5)3<(1)/(2)log_(5)(2x^(2)-6x+7) and log_(3)x+log_(sqrt(3))x+log_((1)/(3))x<6