Question

解下列方程lgx+lgx^2+lgx^3+……+lgx^n=n(n+1)

Answer 1

lgx+lgx^2+lgx^3+……+lgx^n
=lgx+2lgx +3lgx + ... + nlgx
=(1+2+...n)lgx
=n(n+1)/2 * lgx
所以方程等价于 n(n+1)/2 * lgx = n(n+1)
即1/2 * lgx =1
lgx= 2
x=10^2=100

Answer 2

lgx+lgx^2+lgx^3+……+lgx^n=n(n+1)
lgx^(1+2+3...+n) = n(n+1)
[(n+1)n/2] lgx =n(n+1)
lgx = 2
x = e^2

Answer 3

lgx+lgx^2+lgx^3+……+lgx^n=lgx+2lgx+3lgx+……+nlgx=lgx(1+2+3...+n)=lgxn(n+1)/2=n(n+1)

所以,lgx=2

x=100

Answer 4

lgx+lgx^2+lgx^3+……+lgx^n
=n(1+n)/2 *lgx=n(n+1)
lgx=2
x=100