`((log_10 x)/2)^(log_10 ^2 x+log_10 x^2-2)=log_10sqrt(x)`

((log_(10)x)/(2))^(log_(10)^(2)x+log_(10)x^(2)-2)=log_(10)sqrt(x)

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

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

(1)/(2)log_(10)x+3log_(10)sqrt(2+x)=log_(10)sqrt(x(x+2))+2

(1+(1)/(2x))log_(10)3+log_(10)2=log_(10)(27-sqrt(3))

Solution set of the in equality log_(10^(2)) x-3(log_(10)x)( log_(10)(x-2))+2 log_(10^(2))(x-2) lt 0 , is :

Solution set of the in equality log_(10^(2)) x-3(log_(10)x)( log_(10)(x-2))+2 log_(10^(2))(x-2) lt 0 , is :

[log_10⁡(x)]^2 − log_10⁡(x^3) + 2=0

(log_(10)100x)^(2)+(log_(10)10x)^(2)+log_(10)x<=14