log0.5(4-x)>log0.5 2- log0.5(x-1)

Solve for x:\ log^2 (4-x)+log(4-x)*log(x+1/2)-2log^2(x+1/2)=0

The number of solutions of the equation log_(x+1)(x-0.5)=log_(x-0.5)(x+1) is

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

Arrange log_(2) 5, log_(0.5) 5, log_(7) 5, log_(3) 5 in decreasing order.

Solve for x : (i) log_(10) (x - 10) = 1 (ii) log (x^(2) - 21) = 2 (iii) log(x - 2) + log(x + 2) = log 5 (iv) log(x + 5) + log(x - 5) = 4 log 2 + 2 log 3

The equation log_4(2-x)+log_(0.25)(2+x)=log_4(1-x)+log_(0.25)(2x+1) has

Solve for x: a) log_(x)2. log_(2x)2 = log_(4x)2 b) 5^(logx)+5x^(log5)=3(a gt 0), where base of log is 3.

Solve for x :(log)_5 120+(x-3)-2.(log)_5(1-5^(x-3))=-(log)_5(0. 2-5^(x-4))dot

Find the value of (i) (log_(10)5)(log_(10)20)+(log_(10)2)^(2) (ii) root3(5^((1)/(log_(7)5))+(1)/((-log_(10)0.1))) (iii) log_(0.75)log_(2)sqrtsqrt((1)/(0.125)) (iv)5^(log_(sqrt(5))2)+9^(log_(3)7)-8^(log_(2)5) (v)((1)/(49))^(1+log_(7)2)+5^(-log_(1//5)7) (vi) 7^(log_(3)5)+3^(log_(5)7)-5^(log_(3)7)-7^(log_(5)3)

If log(x-y)-log5-1/2logx-1/2logy=0 then x/y+y/x is equal to