Question

110 daca ma puteti ajuta va rog

Answer 1

Răspuns:

Explicație pas cu pas:

Notam log(x;2) = y

log(x;4) = 2log(x;2) =2y,  log(x;8) = 3log(x;2) = 3y

f = 1/(y*2y) +1/(2y*3y) + 1/(3y*4y) +...+1/(ny*(n+1)) =

1/y^2(1/1*2 + 1/2*3 + 1/3*4 +...+1/(n*(n+1)) =

1/y^2(1-1/2 +1/2-1/3 +1/3-1/4 +...+1/n -1/(n+1) =

1/y^2(1 -1/(n+1)) = 1/y^2(n/(n+1)

1/y^2(n/(n+1) =4n/(n+1)

1/y^2 = 4,   1/4 = y^2,   y = 1/2

log(x; 2) = 1/2 = log(x; x^(1/2))

2 =  x^(1/2) = √x

x = 4