Solve: `(1/2)^(log)_(10)a^2+2>3/(2^((log)_(10)(-a)))`

Solve: ((1)/(2))^(log(x^(2)))+2>3*2^(-log(-x))

((log)_(10)(x-3))/((log)_(10)(x^(2)-21))=(1)/(2)

log_(10)3+log_(10)2-2log_(10)5

Solve (x^(log_(10)3))^(2) - (3^(log_(10)x)) - 2 = 0 .

(log_(10)x)^(2)+log_(10)x^(2)=(log_(10)2)^(2)-1

Find the domain of the function: f(x)=sqrt((log)_(10){((log)_(10)x)/(2(3-(log)_(10)x))})

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.

Solve |x-1|^((log_(10)x)^(2)-log_(10)x^(2))=|x-1|^(3)

Solve: |x-1|^((log_(10)x)^(2)-log_(10)x^(2))=|x-1|^(3)

Solve for x: a) (log_(10)(x-3))/(log_(10)(x^(2)-21)) = 1/2 b) log(log x)+log(logx^(3)-2)= 0, where base of log is 10. c) log_(x)2. log_(2x)2 = log_(4x)2 d) 5^(logx)+5x^(log5)=3(a gt 0), where base of log is 3. e) If 9^(1+logx)-3^(1+logx)-210=0 , where base of log is 3.