`(x-2)^(log_10^ 2 (x-2)+log_10(x-2)^5-12)=1 0^(2log_10(x-2))`

((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

The value of p in R for which the equation sin^(-1)((log_(10)x)^(2)-2log_(10)x+2)+tan^(-1)((log_(10)x)^(2)-2log_(10)x+2)+cos^(-1)((log_(10)x)^(2)-2(log_(10)x))=p possess solution is

log_(10)x-(1)/(2)log_(10)(x-(1)/(2))=log_(10)(x+(1)/(2))-(1)/(2)log_(10)(x+(1)/(8))

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