0.25^(x-1)=5^(2x-1)-100

If 25^(x-1)=5^(2x-1)-100 , then find the value of x .

If 25^(x-1)=5^(2x-1)-100 , then find the value of x .

If 5^(2x-1)-(25)^(x-1)=2500 then find x

prove that int_0^(102)(x-1)(x-2)..(x-100)xx1/(1/(x-1)+1/(x-2)+. .1/(x-100))dx=101 !-100 !

Prove that int_0^(102)(x-1)(x-2)(x-100) x(1/((x-1)+1/((x-2))+1/((x-100))dx=101 !-100 !

Prove that int_0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2) +.... .+ 1/(x-100))dx=101 !-100 !

Prove that int_0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2) +.... .+ 1/(x-100))dx=101 !-100 !

int_(0)^(102)(x-1)(x-2)dots(x-100)xx((1)/(x-1)+(1)/(x-2)+.(.1)/(x-100))dx=101!-100

Vertices of a variable triangle are (3,4); (5costheta, 5sintheta) and (5sintheta,-5costheta) where theta is a parameter then the locus of its orthocentre is a. (x+y-1)^2+(x-y-7)^2=100 b. (x+y-7)^2+(x-y-1)^2=100 c. (x+y-7)^2+(x+y-1)^2=100 d. (x+y-7)^2+(x-y+1)^2=100

{:("Column" A ,, "Column" B), (225x^(2) - 625 y^(2) = ,, (a) 25(x-2) (x-2)), (x^(2) - x - y - y^(2) = ,, (b) 25(3x- 5y) (3x + 5y)), (x^(2) - x - y^(2) + y = ,, (x + y) (x - y- 1)), (25x^(2) - 100 x + 100 = ,, (d) (x - y) (x + y -1)), (,,(e) (x + y) (x + y - 1)):}